Many players fear speed chess because of potential to hurt your play quality, but I believe that speed chess can be useful every now and then IF utilized correctly. Unfortunately, many do not make the most of speed chess...
First off, longer time controls is preferred because it gives you some "extra thinking time." In this time control, you aren't "rushed" and can use that "extra" time to blunder check, come up with game plans of your own, anticipate opponent plans, find a good move but then look for a better one and many more things that helps with long-term improvement. Speed chess like 3 min. blitz is simply nowhere near enough time to come up with all of this...well, at least not when starting out anyway. Experienced speed chess players like @Hikaru can play speed chess well AND do all the things I mentioned because they "save time" elsewhere. By "saving time" I mean that they have many patterns in their repertoire, have lots of opening theory memorized and can also make use of premoves efficiently. Let us not forget though, these players are generally also strong chess players at longer time controls.
I see the "problem" with blitz being mostly conditioning your mind to moving quickly (which is a weakness if that is your habit under longer time controls if you can't easily adjust) and also not enough time to "think" and calculate some ideas out as much as might be useful. However, speed chess does also have some benefits (as your coach mentioned) like playing more games in the same time frame or getting more "opening" experience because you get to play more than with one or two long games.
I recommend at least 10 min chess and maybe even longer if you can afford it. I also am a strong believer of mixing up your time controls. Similar to you not wanting to only condition your mind for blitz, you don't want to condition your mind for only long time control chess. Whatever your "main time control" of preference is, I find it beneficial to also vary.
If your "main" time control is 10 min chess (most popular chess.com time control), then I'd also play several longer games of 20 min+ or even 30 min+ if you can. If your "main" time control is classical chess with a game lasting several hours long, then play a few 5 min blitz games here or there 
By doing this, you do not condition your mind to ONLY think at a certain pace and this makes adjusting to different time controls easier to do.
I started to play chess to about 5 months, at first I mainly played 10 minutes rapid game. After that I feel a little bit stuck (at around 1450-1500), then I saw some comments online that playing speed chess could cultivate your instinct (and also my coach recommended so that I could play more games in limited time). Thus I play a lot of 3-0 blitz, but stuck again when I reached 1400-1450. What do you guys suggest? Shall I play rapid game again or should I stick with blitz chess? Thanks a lot.