This is going to be a really short review because I don't want to overly complicate why I like this anime. The big four reasons I like this show is because:
1. Characters. The characters to me seem like they have a lot of depth to them. This anime is very close to how people think and feel. Certain characters that think they aren't good enough is very common of anime. But it's usually to some drastic degree, but the emotions seem very mundane and normal. That's the beauty of it, it gives a very simple view of the typical person's psyche. Most romances don't really focus on the depth of emotion regarding themselves. It's actually refreshing for an anime to not be over the top and actually seem like they are normal everyday human beings.
Also, this shows paints the side characters almost just as important as the main characters. They aren't some barely mentioned characters for comic relief, but seem like they really add to the story. It is very beautiful to see how much time is put into each character.
2. Art. This is a rather silly point, but I think Horimiya has the best art I have seen in any romance anime. It is just breathtaking.
3. The mundane feelings of everyday life. I know I mentioned this in the fist point, but I like how normal the anime feels. It doesn't feel like too many things are over the top crazy. Just normal people that fell in love. Many other romances are so freaking over exaggerated, so something like this just feels refreshing.
4. My last point is that there are barely any "misunderstandings" in this anime. One reason why Kimi Ni Todoke was so hard to watch is because six episodes would pass to where the MC and others thought they hated each other, but if they had simple social skills, could have been figured out in one. Horimiya has misunderstanding in it, but they resolve it the same exact episode. I can finish every episode and feel pretty happy about it, rather than the stupid long, terribly drawn out, misunderstanding.
Regarding Horimiya's hate: Not to be rude to most reviewers that rate this anime a low score, the arguments for them are kinda weak. It makes sense that not everybody will find an anime to be good, that's fair. But it seems like most people just try to hate on popular anime. Any anime that is overhyped, it seems like a specific people group will try to hate on it for no apparent reason. They try to compare it to anime like Kimi Ni Todoke, or Kaguya-Sama, but they all serve a different purpose in how they are written. But you're entitled to your own opinion. Whoever reads this, try not to let reviews make or break if you watch an anime or not, find out for yourself =)