One, the only way they can screw it up if they change and remove aspects of the old one. Dont talk for ff7 fans if you think being a true ff7 means hate SE more to not want one.
Two. Its not about reliving the memory. Its having a new one.
It's not about hating SE. It's about understanding that the quality of their work is not good enough to have any kind of a remake. And knowing SE they probably WOULD end up changing things removing aspects or the original.
And if it turns out like crap you will have a horrible memory of the game that was based off of a beloved game. To me: a remake right now would be a bad idea no matter how you look at it. It would be a miracle if SE remade FFVII right now and they did it well.
It wouldn't be perfect, no. But I don't think SE would screw the game up either. With a goldmine that VII had proven to be, they would want to make it as perfect as possible, and that would mean following the original to a T, with some inclusions for retcons, voices, graphics, incomplete portions. Why would the game play need an overall? It was perfectly fine.
The thing is, I don't think SE is at a stage where they can perfect a game like the remake of VII. I honestly don't. And if said game were to take away time and effort into future games then I'm against it. My problems with the FFVII remake vary. Obviously I have three points: FFVII has had enough attention, If they remade it from scratch it could be a disaster, and it could take away time and money from developing a new game.
Also in your post you said that SE has remade games and did it well. Weren't those mainly just ports and remastering? They were NOTHING on the scale of what a FFVII remake on a PS3 or PS4 would be. My guess is that SE would look towards making a full blown remake. And that's where it could tarnish thing for the fans.
Personally, that's not my main concern. My main concern is for the other FF titles that are being forgotten, and in many cases are a lot better games than FFVII. I'm not saying those games should necessarily be remade. But I would prefer spinoffs and such for them....