Yes, there is.

There are three problems, broadly speaking.

Conflation of borrowings with origins.

It's almost inevitable that some elements of a celebration like Easter are 'borrowings' from other traditions/practices/celebrations. But borrowings are not origins. To take the poster to task that you linked, rabbits, eggs, etc., are all Easter traditions, but they appear historically to have little to do with the origins of Easter as a celebration.

Thinking that all history happened in English.

I'm not even joking that this is a problem. 'Easter' is only 'Easter' in English, and Bede is the only source that suggests it was an adaption of the Anglo Saxon Eostre, for whom I'm not even sure we have any other source. Do people really think Easter was invented in the middle ages by the English? We're talking about a celebration that dates to late antiquity and was widely practiced across Christian groups in various languages. My other pet hate is people who think there is a pun on Sun and Son.

What you celebrate is what you celebrate

Sometimes these types of claims are made with this kind of fallacy: "x, y, z comes from pagan traditions, therefore this is really a pagan celebration of (spring)". but if you ask anyone celebrating Easter as a Christian, a large set of responses is going to be "We're celebrating the death and resurrection of Jesus". There's a sociological argument that what they are celebrating is waht they say they're celebrating. That's why the argument "no, it's really pagan celebration of a, b,c" is a kind of origins-fallacy.

I'm really happy to discuss specific origins of particular elements of Christian celebrations, if you want to ask about them, but most of the broad-sweeping claims made about these festivals are bad history and uninformed atheist apologetics.

As you rightly suspect, the problem with most of these arguments is that they assume that 'paganism' and Christianity are two equal and opposing religious institutions - two different churches that hated each other. And the Christian church beat the pagan church and stole all its holidays.

The problem is, 'paganism' wasn't really an ism. It's a catch-all term for a variety of beliefs and practices about the workings of the natural and supernatural world. And many of these beliefs which predate Christianity were accepted in antiquity by both Christians and non Christians. For example, the belief that certain springs and wells were holy - everyone agreed on this, so when local villagers became Christian, they kept making offerings at their local sacred spring. Did that mean they were still secret pagans or bad Christians? Not really - it just meant that they agreed with their pagan ancestors that the spring was special. That belief didn't have to be exclusive to one faith or the other, because paganism wasn't a church - it was a collection of beliefs and practices, many of which were considered perfectly compatible with Christianity.

Most of the borrowings are best explained in these terms. Christians and non-Christians shared certain assumptions about which days were especially holy, which places especially magical, and which kinds of spells and potions were the best way to manipulate the rain into falling and which effective at keeping beer from going sour. These weren't considered, by the average person, to be religiously-loaded issues; they were just facts about how the world worked, and could be engaged with by anyone regardless of their creed. Some church leaders took issue with some of these practices and condemned them in their sermons, but in general, just as most modern Christians agree with atheists that science is real, ancient Christians usually agreed with pagans that there was something magical about springtime.

So it wasn't so much that Christianity borrowed or stole pagan holidays and traditions. They shared them, because they both agreed that those days and rituals were important, even though they explained that importance in different ways.