I have always thought the lesson here is to be careful when insulting those with a great deal of power over you. Pope Urban VIII was originally a patron and supporter of Galileo:

>...Indeed, although Galileo states in the preface of his book that the character is named after a famous Aristotelian philosopher (Simplicius in Latin, Simplicio in Italian), the name "Simplicio" in Italian also had the connotation of "simpleton."[55] Authors Langford and Stillman Drake asserted that Simplicio was modeled on philosophers Lodovico delle Colombe and Cesare Cremonini. Pope Urban demanded that his own arguments be included in the book, which resulted in Galileo putting them in the mouth of Simplicio. Some months after the book's publication, Pope Urban VIII banned its sale and had its text submitted for examination by a special commission

https://en.wikipedia.org/wiki/Galileo_affair

It wasn't his theory, it was that he presented it in the form of a dialogue with a character who was an obvious stand-in for the Pope, and then made that character sound like a complete idiot.

The heresy charges were an excuse to punish him for being disrespectful. He'd gotten approval from the Pope to publish; he would have been fine if he'd just been polite.

Obviously that's still petty and unjustified, but science denial wasn't the real reason for it.

He indirectly called the Pope a simpleton, and the Pope took offense.

The Catholic Church was quite tyrannical about opining on matters of theology. Heliocentrism vs Geocentrism, which discussed in terms of whether it's really true or not (as opposed to merely an interesting mathematical model), was considered to be this. That didn't mean that the church was unwilling to discuss it, but that they wanted the public discourse to be controlled to avoid it seeming to conflict with their domain, at least until they could be convinced (and Galileo's main problem is that he could convince very few people inside and outside the church, due to lack of available evidence) and change their official line themselves.

The other problem for Galileo was that he did basically just piss off a bunch of people (he was, by all accounts, very good at publicly dunking on people, whether they were right or wrong. He'd be a natural on modern social media). There was a large group who basically started conspiring against him, trying to implicate him in going against the church, and then his book (which was 'approved' through a very chaotic, almost comical sequence of bad timings and missed communication) managed to insult and piss off the Pope, who was previously a very close friend.

So, ultimately the broad thrust of the situation is not changed: the church was ultimately wrong and unreasonable in their demands, and Galileo was ultimately correct in rejecting Geocentrism, but the church was more reasonable than generally implied in the simplified telling, and Galileo was a lot less correct, and especially lacked good rational arguments and evidence for his specific model.

> why Galileo was placed under house arrest

Galileo's friend Barberini became Pope and asked Galileo to write a book. But Barberini became paranoid about conspiracies and thought it had seditious, secretly-critical undertones.