I realize Twitter isn't exactly the best place for nuanced reviews because of the character limit, but wow, those points really summarize John in a nutshell.
The first three are all purely visual. And if you want to play angry feminist like John does, seems kinda problematic to say something is good solely because there are women in it. Feels like it's playing into the male gaze. It'd be one thing if he was saying something about their characters/acting performance, which even with Twitter's limit wouldn't be hard to clarify.
Then the last two show how much John loves victimization. I don't want to sperg too much, especially since I imagine most people are familiar with the early Terminator franchise, but a big problem people have with the third movie is the ending. The second movie was largely about the concept of fighting fate/the future can change if you're willing to fight for said change. Not exactly a new concept or anything, but I also wouldn't say the movie is all sunshine and rainbows, I mean, Arnold still has to sacrifice himself at the end to give humans a chance.
But the third movie ends with them doing everything they can to avert disaster only for it not to matter because it turns out, fate is a thing and you can't actually change the future. Again, not a new concept by any means and while there's nothing inherently wrong with that as an ending in a standalone piece, it's kinda questionable to do when, granted this is with a fair amount of hindsight, this is like, what the halfway point of the Terminator franchise? Again, they clearly didn't know how many Terminator movies there would be after this, but if you want to get across that fate can't be changed in a movie that's largely about traveling to the past to change the future, well, you're kinda setting those movies up for failure.
To get a little more nitpicky, I think both T1 and T2 have plenty of fairly iconic lines. So much so that the Terminator movies today are still referencing them. And it isn't just the dialogue, there's some pretty iconic scenes that, again, still exist in the pop culture sphere. Despite "having better CGI" I can't think of anything iconic about T3's scenes or any memorable lines. I haven't seen the later Terminator movies, but do the new characters they introduce in T3 even show up or get mentioned in the later movies?
Nope, not once to my recollection, and I've seen them all (except Dark Fate because lolno). The biggest issue with the Terminator franchise is that every time they try to reboot the franchise, it doesn't go as well as the studio wants, they chicken out of any sequels, and then they reboot it again with a completely different continuity.
Terminator Salvation was probably the best path forward for the franchise, and the only post-T3 sequel I would consider passable in any way. It was a direct sequel to T3, and showed a part of the Terminator timeline we had only really glimpsed before, the actual war against the machines. It was originally going to be the start of a new trilogy, which I'm guessing would have ended with the final battle and Kyle Reese being sent back to stop the first Terminator, closing the loop on the series. Sadly, it didn't do too great at the box office, then the production company filed for bankruptcy and that was the end of that.
Terminator Genisys comes along a few years later and tries to restart the timeline completely by going all the way back to the first movie and saying "lol this didn't happen anymore because we sent ANOTHER Terminator but a good one to stop ANOTHER Terminator from killing Sarah Connor even earlier and now he's good guys." And then there's more time travel and John Connor is a robot zombie and...fuck it, I'll just let Scientist Man explain.
It was also going to be the start of a trilogy in its new rebooted continuity, but it was also not as much of a success as the studio wanted, so those plans got axed.
Then along comes Terminator: Dark Fate, which
also tried to restart the timeline. This time, it ignored Genisys, kept the first two movies intact, but then
fucking killed John Connor in the first couple minutes. Then it sets up effectively the same storyline as the first movie, just with all the names replaced (it's a different AI, it's different Terminators, etc.). And you can probably guess the rest: planned trilogy, poor performance, plans scrapped.
As you said, T3's plot and ending might have worked in a standalone movie, but it really wasn't satisfying for fans of the first two movies as it undercut the crux of their plots completely. It certainly wasn't good just because it had an "unhappy ending" like John claims. And besides, we all know why John really liked it, he was probably masturbating to the thought of being a sexy killbot in the theater.
