From a general business standpoint, consolidation in any industry tends to not benefit the consumer. An extreme example of that is broadband internet. In most markets, consolidation has made it so you realistically have one serious option for internet/cable in your area, and then a couple of alternatives. As a result, broadband pricing in general is absolute fukking trash. The argument being made is that while this specific sale doesn't get
Microsoft to that level, it does set precedent if they want to make another purchase like this again later on, that the sale should be harder to push back on.
Sony's problem is that while Activision/Blizzard doesn't publish a TON of games, they games they publish tend to be pretty heavy sellers. As it is now, they're good with their 30/70 split on sales made via PSN for those games, since they're going to a third party that doesn't actually compete with them. This purchase would change that so it's a 30/70 split with the 70 going to a direct competitor, essentially forcing Sony into a situation where they're essentially funding Microsoft's efforts to build out XBox as a platform, all while Microsoft could theoretically pull those games from Sony at some point, or at minimum, just offer those games as part of Game Pass.
Microsoft's main issue is that, while they've invested in a lot of studios recently, not many of them have games ready to keep a steady stream of hits coming. Acquiring Activision/Blizzard gives them an immediate boost, since they will have acquired what is effectively a game factory, since CoD always finds a way to release yearly.
Where the issues come into play is that both sides are playing the PR game, and essentially trying to weaponize the consumerbase against the other side with pretty shytty, bad faith arguments.
Add in folks online more than happy to engage in dumb console wars, and you've got fukkery that came together quicker than instant grits.
