Damore shouldn't have shared his opinion (the way he did) because there is a huge gap between what he claims to aim for and what he actually does. He claims that open discussion, diversity and helping to improve the situation are what important to him. But in practice he does right the opposite: creates a hostile working environment with perverted reasoning, loads of bias perpetuating harmful stereotypes, ignoring how his tone will affect others and pretty agressive promotion of these views instead of politely sharing a well thought out intellectually honest opinion.
Given the sensitivity of topic he tries to discuss, 'how' is an extremely important part of 'what', still he manages to twist his declared 'what' to the 180 degree with his 'how'. It seems that he was fired exactly for showing strong intention to continue the promotion of his highly biased opinions while completely ignoring what it actually does to people around him. Disproving the memo wouldn't help to stop it if this was the case.
First, you've crossed over from criticizing delivery into criticizing content, so it's clear that's actually the part that offends you. What you're saying is that Damore shouldn't have delivered his opinion unless it was first made to match something reasonably close to your own opinion. There is nothing inherently "dishonest" or "perverted" about Damore's memo; that is a subtext that you are choosing to read in because you disagree with its conclusions.
If Damore had pined on the tragedy of the modern economic structure while exhaustively disclaiming every potential discriminatory implication before he began the memo, I guarantee people would've read just as much "intellectual dishonesty", "perverted reasoning", and "loads of bias" as they did now. In fact, they very likely would've read more, taking the content that initially appeared friendly to their POV as a sign that Damore had malicious intent and that he was attempting to hoodwink people by pretending to be "on their side".
As discussed below, if someone wants to dismiss something they don't like, airy, abstract terms like "perverted reasoning" will get bandied around no matter what. These terms are great precisely because their subjective interpretation allows the writer to sound semi-credible in their condemnation without having to specify further.
Damore was fired because once this hit the mainstream press, it was the only way for Google to preserve a strong defense against inevitable discrimination suits.