Perhaps a climatologist would be better able to answer the differences in climate from five thousand years ago to today. However, historically Egypt has been a hot spot for agriculture because of the Nile river. The Nile, flowing from Lake Victoria in the south, used to have a higher flow rate before water diversion programs and dams were created along its course. The predictable nature of the Nile's floods made it an ideal place for larger agricultural communities. The climate in the area, namely the mild winter from November to April and the hot summer from May to October gave ample time for planting and harvesting around the annual floods which also refreshed the soil with nutrients, allowing for agriculture to develop without ruining the soil or leaving fields fallow.

Today, the population of Egypt is ~82 million. Compared to ancient times when the population was signficantly less (perhaps an ancient Egypt expert can provide a verifiable source for the peak population of ancient Egypt, I looked but was unable to find anything scholarly to cite, most seem to be estimates). Couple this with the changes to the river over five thousand years and humans exercising control over the floods, and you have a signficantly reduced ability to provide food to a signficantly larger population.

Why did production not grow to match the population?

Egypt is severly limited in that, its portion of arable land is essentially that next to the river Nile. 96.3% of Egyptian land is desert. As you can imagine, once all this land has been farmed, Egypt has no alternative but to import food. Finally, since 1960 Egypt's population has trebled in size.

Like other comments suggested, the population plays a significant factor to agriculture. It's also important to note that the pharaohs' governments collected crops as a form of taxes. The crops were stored away to be used in times of famine (though they benefitted the royal family moreso than the general population).

When it was absorbed by the Romans, Egypt became a primary breadbasket for the empire, and exported most of its wheat to other areas of the empire.

Source: The Rise and Fall of Ancient Egypt by Wilkinson

People are making good points about the limitations on agricultural production in Egypt relative to the growth in population, but it'd be curious to know more about how the land is cultivated (I don't remember seeing a whole lot of industrial farms in Egypt) as well as what is actually grown. Egypt grows a lot of cotton, I believe. You can trade that cotton for foodstuffs, but you can't eat it.

Point is that that I doubt that Egypt could grow enough food for 82M, but they could probably grow a lot more food than they're growing now.

There have been some good answers here about the huge growth In population, the 19th century shift to cotton production (and industrialization.) One issue i haven't seen mentioned is the system of food subsidies that Egypt has put in place which absurdly skews the market for basic food stuffs. Bread is subsidized to such an extent that farmers feed an average of 80 kilos of bread per year (7-8% of their total bread purchases) to their animals because it's cheaper than animal feed.

I know normally this would be a 20 year rule political issue but this has actually been the case for decades.

Edit: source