Sweeney (the CEO of Epic) says that he wants competition with Steam, but many of his actions point toward that he really just wants to be the guy at the top (ie, he wants to be the monopoly instead of Valve). He's taken a fair number of anti-consumerist stances, which vary from understandable to clearly anti-competitive.

Epic is known for making exclusivity deals with 3rd party studios in which Epic bribes the studio with money, and in exchange, the studio does not release their game on Steam for 1 year.

At several points, this occurred after a studio already said that they will release on Steam, and the studio would have to walk back and delete their Steam listing.

Iirc, at one point Epic bought out a studio and had them remove the Steam listing for an already-released game, causing the game to be unplayable for people who had already bought the game

Edit: this apparently happened twice (Unreal Tournament and Rocket League), but it appears that the games still work for the people who bought it. I think the concern was actually that Steam players would lose functionality due to not being supported anymore after the unlisting

The Epic Game Store released in a non-functional state, and development on it is extremely slow. The first impression of the broken store likely still influences many people's impression of the store. But it's still missing many features that many gamers want to see in a store.

There were various rumors when the store first launched that it contained spyware. My understanding is that those rumors never fully got disproven, especially since some of the claims were supported by at least some evidence

Epic does not support Linux, and Sweeney has openly said that he does not plan to support Linux until it becomes more popular. He did immediately jump on board with supporting Arm though, which caused a lot of Linux gamers to think that he just doesn't want to support Linux

Sweeney is a pretty abrasive person and iirc he made a lot of concerning statements on his social media. Several of them (as mentioned above) indicate that he wants to dethrone Valve so that he can be the monopoly instead

Overall, many gamers are in support of more competition in the game store space. Unfortunately, many gamers also think that Epic is an untrustworthy competitor, and they believe that Epic has a serious chance of making the gaming industry worse if they become more popular. As a result, many would prefer for Steam remain the monopoly rather than to take a bet on Epic.