Climatological data suggests that the reign of Ramesses II was a remarkably wet period followed by a much drier period linked to a drying up of the Nile. These conditions would have been ripe for an algal bloom and the subsequent infestations of frogs, lice, and flies. Some scholars have used this evidence to suggest the biblical plagues were based on actual events.
Professor Augusto Magini, a paleoclimatologist at Heidelberg University's institute for environmental physics, said: "Pharaoh Rameses II reigned during a very favourable climatic period.
"There was plenty of rain and his country flourished. However, this wet period only lasted a few decades.
After Rameses' reign, the climate curve goes sharply downwards.
"There is a dry period which would certainly have had serious consequences."
The scientists believe this switch in the climate was the trigger for the first of the plagues. The rising temperatures could have caused the river Nile to dry up, turning the fast flowing river that was Egypt's lifeline into a slow moving and muddy watercourse. These conditions would have been perfect for the arrival of the first plague, which in the Bible is described as the Nile turning to blood.
Dr Stephan Pflugmacher, a biologist at the Leibniz Institute for Water Ecology and Inland Fisheries in Berlin, believes this description could have been the result of a toxic fresh water algae. He said the bacterium, known as Burgundy Blood algae or Oscillatoria rubescens, is known to have existed 3,000 years ago and still causes similar effects today.
He said: "It multiplies massively in slow-moving warm waters with high levels of nutrition. And as it dies, it stains the water red."
The scientists also claim the arrival of this algae set in motion the events that led to the second, third and forth plagues – frogs, lice and flies.
Frogs development from tadpoles into fully formed adults is governed by hormones that can speed up their development in times of stress. The arrival of the toxic algae would have triggered such a transformation and forced the frogs to leave the water where they lived. But as the frogs died, it would have meant that mosquitoes, flies and other insects would have flourished without the predators to keep their numbers under control.
These scientific explanations are not conclusive, and it's quite possible that the plagues are literary imaginings of catastrophes feared by any agrarian society. Turning to Egyptian sources for comparative material, many of the plagues have parallels.
The imagery of the Nile turning into blood as a result of political unrest, the first plague, is known from the Admonitions of Ipuwer, a Middle Kingdom text preserved in a New Kingdom copy.
Lo, the river is blood
As one drinks of it, one shrinks from people
And thirsts for water.
Ipuwer also mentions the death of children (compare to the 10th plague)
Lo, great and small (say), "I wish I were dead"
Little children say, "He should not have made me live!"
Lo, children of nobles are dashed against walls,
Infants are put out on high ground.
and complaints of cattle (compare to the 5th plague).
Lo, all beasts, their hearts weep,
Cattle bemoan the state of the land.
Such doom-and-gloom pieces, which claim that various catastrophes and social upheavals occurred during times of political decentralization, are not uncommon in Egyptian literature. The Prophecy of Neferti, for example, discusses the withdrawal of Re and a darkening of Egypt as a consequence of political instability, which one can compare to the 9th plague of darkness.
Re will withdraw from mankind:
Though he will rise at his hour,
One will not know when noon has come;
No one will discern his shadow,
No face will be dazzled by seeing him,
No eyes will moisten with water.
The Complaints of Khakheperresoneb contains a similarly mournful account of recent events.
I meditate on what has happened,
The events that occur throughout the land:
Changes take place, it is not like last year,
One year is more irksome than the other.
The land breaks up, is destroyed,
Becomes a wasteland.
These works of literature were created by the elite for elite consumption and reflect a political-propagandistic aim by contrasting the (supposed) sorry state of affairs without a unifying king to the strong, centralized government and prosperous Egypt of the Middle and New Kingdoms.
As for a proliferation of frogs, they would have been a rather irritating nuisance -- but only a nuisance. Frogs are neither dangerous nor destructive, but their noise and invasiveness would have been irritating. The passage notes the frogs crawled into bedrooms, into kitchens, and even into ovens, the last place you'd expect to find a frog.
Accounts of animals invading homes are quite common in ancient Near Eastern literature, unsurprisingly nearly always a negative event. Tablet 44 of the Šumma alu omen series, for example, contains omens for the actions of wild animals.
If a fox enters a man’s house, the hand (of a god) will affect that house.
An Old Babylonian letter contains a more frightening example, a lion stuck in the upper room of a house.
A short time ago I wrote to my lord as follows: "A lion was caught in the loft of a house in Akkaka. My lord should write me whether this lion should remain in that same loft until the arrival of my lord, or whether I should have it brought to my lord." But letters from my lord were slow in coming and the lion has been in the loft for five days. Although they threw him a dog and a pig, he refused to eat them. I was worrying, "Heaven forbid that this lion pine away." I became scared, but eventually I got the lion into a wooden cage and loaded it on a boat to have it brought to my lord.
As a final example, animals were perceived as agents of impurity, which would have been a particular vexation for temples and palaces, where ritual purity was strictly regulated. The Hittite "Instruction for Temple Personnel" outlines the consequences of tolerating a pig or dog in the kitchen.
If a pig or dog touches the wooden utensils or the ceramic wares that you have, but the kitchen foreman does not throw them out, then the deities will give him feces and urine to eat and drink.
As BS Child's wrote in his commentary on Exodus
In the long list of plagues which Moses evoked on the Egyptians, frogs would certainly be accounted among the least fearful
So you're right in noticing that this is a strange plague to inflict as frogs are not natural enemies of man... Generally the context of the plagues has to be Exodus 12:12 where God announces that he will strike judgement against the Egyptian gods - that's how the plagues are to be understood according to the text, so any answer is likely to be found there in both a literary and theological sense.
Literary-wise, the plague of frogs introduces concepts that are going to trouble the Egyptians later on. God strikes the Egyptians with frogs, and the frogs cover the land, and when they die, they're gathered up in heaps. The same language is used when the Destroyer will strike down the first-born Egyptians (12:23), the waters of the Re(e)d Sea will cover the Egyptian army as they attempt to cross, and their bodies will be heaped up on the shoreline (14:30), so the language of the frog plague presages things that will happen in the future (not that that is any use to the Egyptians). The frogs also invade pharaoh's house which means he has to come to Moses to sue for relief, forcing the ruler to come to his opponent, a harbinger of what will happen at the end of the plague cycle.
Looking at other Ancient Near Eastern vassal treaties, Van Seters suggests that the attack on the Nile and the plague of frogs are distinctly attacks on what is most important to Egypt (the Nile) in the same way that in the treaty between Assyria and Tyre, the three west-Semitic deities are called to bring disaster on the ships of Tyre. This moves us closer to the classical interpretations of the plagues, which are often seen as attacks on Egyptian gods (cf Exodus 12:12) but that isn't as clear as it could be. It is true that Heket was an Egyptian god frequently identified with frogs (for their fertility) and there is a certain thematic neatness to having the frogs (fertility) die, rather than having them removed (presumably to the Nile as requested), but I suspect that might be too of an obscure meaning for the average Israelite, and the Egyptians didn't look at a frog and go 'It's Heket' or a cow and treat it with respect as a reference to Hathor. It's easier to see these are supernatural attacks on what is primarily important to the Egyptians - the plagues only affect the Egyptians, not the Israelites just next door in Goshen. It's Yahweh that rules Egypt through Moses and his staff, not the pharoah and his ḥḳʒ (scepter).
A number of people did/do follow the Greta Hort theory, that there is a natural sequence to the plagues - the Nile goes bad, frogs come out of the Nile as a result, they then die, subsequently causing pestilence etc., but that only deals with the first 6 plagues - the last 4 don't really follow that sequence. Of those 4, only 3 of them are natural and occur in Egypt, the last one (the death of the first born) is definitely supernatural, and I don't really know of anyone who still follows this naturalistic form of plagues at least in the academic world as it's generally seen as a literary/theological event. It's also problematic in terms of the text because the animals are killed in the pestilence plague (9:6) but then are killed again in the hail plague (10:25ff).
Some prefer to look at the plagues in terms of hyper-naturality, meaning that the natural borders of creation have gone wild - an opposite to the order of Genesis - and this is borne out by several references in the text that theses things 'had never been seen before, nor ever shall be again' (10:14, 10:6, 9:18 etc.,) and I think this is a better reading - the plagues are supernatural afflictions showing the power of Yahweh over the (then) Israelite enemy (although they're not properly Israelites yet, and even proto-Israelites might be problematic but that's another discussion).
In short, there's no particular reason why frogs, there's nothing significant about them except they're part of the Egyptian background. It's certainly reasonable to interpret it as part of the attacks on what is important to the Egyptians (the Nile) but there is a definite literary/theological reason for it rather than a naturalistic one.
Some random observations:
If you read the text carefully, Moses normally prays to God to end plagues - the frog plague is the only one where he 'cries' out to God. Lerner suggests that the reason for this is that frogs are noisy and a plague of frogs would be incredibly sonically annoying ;) However, one Samaritan Pentateuch variant suggests the frogs descended on the people themselves, which visually is much more interesting.
Some older Jewish commentators differed in what they thought the word tzefarde'a meant - the generally accepted meaning is definitely frog, but there are some other variants where the word means 'crocodile' which is a much cooler visual image than frogs, but alas, doesn't really fit what the text says they did (climbing into cooking bowls etc.,)
Sources:
Benjamin, Tammi, and Marc Mangel, ‘The Ten Plagues and Statistical Science as a Way of Knowing’, Judaism, 48 (1999), 17–34
Blumenthal, Fred, ‘The Ten Plagues: Debunking Egyptian Polytheism’, Jewish Bible Quarterly, 40 (2012), 255–58
Childs, Brevard S., Exodus: A Commentary (SCM, 1974)
Fretheim, Terence E (Erling), ‘The Plagues as Ecological Signs of Historical Disaster’, Journal of Biblical Literature, 110 (1991), 385–96
Hendel, Ronald, ‘The Exodus in Biblical Memory’, Journal of Biblical Literature, 120 (2001), 601
Hort, Greta, ‘The Plagues of Egypt’, Zeitschrift Für Die Alttestamentliche Wissenschaft, 70 (1958), 48–59
Lerner, Berel Dov, ‘Crying out about Frogs’, Vetus Testamentum, 60 (2010), 662–63 https://doi.org/10.1163/156853310X530488
Slifkin, Nosson, ‘Tzefardeaʻ: Frogs or Crocodiles?’, Jewish Bible Quarterly, 38 (2010), 251–54
Van Seters, John, ‘The Plagues of Egypt: Ancient Tradition or Literary Invention?’, Zeitschrift Für Die Alttestamentliche Wissenschaft, 98 (1986), 31–39
Hoffmeier, James Karl, Israel in Egypt the Evidence for the Authenticity of the Exodus Tradition (New York: Oxford University Press, 1999)