The left wanted mandatory reselection, which would allow local members of all political stripes more say in who they spend their time campaigning for rather than mates/ideological bedfellows of the leadership being foisted on CLPs (especially in safe seats), denying local activists the chance to represent their own constituencies. The reason that was seen as a bad thing by the right is because they (justifiably) have no faith in their ability to attract like-minded people to join the party or to win over existing members. In practice it probably would lead to a more left wing PLP, but it would also lead to one much more in touch with local communities instead of one dominated by well-connected career politicians who barely know the place they're mean to represent. During the Corbyn years my MP resigned and the left NEC pulled some skulduggery to keep a local candidate off the shortlist and set up their preferred candidate for the win. That shit is annoying and counterproductive regardless of who is doing it.
A lot of your post is reflective of how different the bar is for left and right. Corbyn and the left were demonised as Stalinist for trying to make the party more accountable to the activist base which it relies on to win elections, Starmer and the right get a free pass for actively purging left wing members and trying to rig internal elections. After a leadership election where Labour staffers allied to the right engaged in an active campaign to block left wing Labour members from voting, Corbyn came in and made legitimate attempts to reach out to the party and include a range of views in his Shadow Cabinet. After a leadership election where the left backed Starmer in huge numbers, he responds by going back on every assurance he gave them and sacking one of the two left wing MPs in the Shadow Cabinet from the Education brief for the crime of being too aligned with the interests of teachers. The same Labour members who voted Corbyn in voted in Watson, a clear sign that they were willing to work with centrists, Watson immediately turned round and started slagging them off in the media and calling for them to be kicked out of the party. The only crime the left had committed at that point was daring not to vote for a group of people who had no vision and a massive sense of entitlement.
I mention the manifesto because Starmer's pitch as party leader was to build on the 2017 manifesto, it was one of his 10 pledges that convinced many on the left to put their faith in him. Again, he's repaid that faith by tearing each and every pledge up, marginalising the left of the PLP and pressing the purge button on left wing members. I'm not gonna back anything Lavery or McCluskey have said as more often than not I disagree with both, but the average left wing Labour Party member has every reason to distrust and dislike the centre/right of the party - they have consistently demonstrated from day one that they don't play fair and that they never had any intention of trying to win an election whilst Corbyn was in charge. On the other hand, the left, barring a vocal minority, has repeatedly attempted to engage in good faith with the rest of the party and every time it's been thrown back in their face. The right can lie, cheat and steal and undermine the party's electoral prospects with impunity whilst the left is expected to stay quiet, have no input and go out to campaign and vote for people who want them out of the party.
That's why it's annoying when people come out with things like 'both sides needs to compromise'. The left has compromised, a lot of us voted for Watson in 2015 and Starmer in 2020 precisely because we were willing to compromise. Our mistake was being daft enough to think the the right was capable of doing the same.