I think it's rather inept & cruel of your teacher to tell you your playing is void of emotion. That's subjective, and is intangible so very hard to know how to fix, or know when you've fixed it. Even if you did, you'd only have been satisfying your teacher. I'm really sorry to hear it made you quit.
I find Bon Jovi utterly devoid of emotion or excitement, but a lot of people really love their music so they must find something enjoyable in it. If I was Jon Bon Jovi's tutor, I'd be tempted to comment on his emotionless performances but probably would hold back so as to let him be what he is. Excuse my arrogance there, but that's kind of my point: We're all allowed an opinion, especially with the arts, and we may not all agree :-)
There are other examples I could list but it'll start to sound like me bitching lol
A thing not to do (at first):
The current trend is to sing a zillion notes around the tune when one or two would have done. Even that can sound mechanical (and sometimes awesome too). If you'd like to sing like that, it's probably best to work on the basic stuff first and then embelish it. But I just wanted to say that this style isn't a replacement for 'singing with feeling' - call me cynical, but it's just more notes.
You haven't said what kind of music you play so it's a bit difficult to give a 'technique' but one thing that gets the rush of passion for me is when my band (rock bass/drums/guitar - I'm guitar & vocals) is throwing out a huge sounding tune which hits you in the chest- literally. So thating with that ..
- Thing 1: Loudness.
I think there's some kind of instinctive excitement in hearing loud noises like drums and guitar. The sound thumps you in the body as well as your ears, and gets the adrenalin going.
For me, that excitement pushes my mood up and I just have to let it out with the sining !
Note that loud doens't necessarily mean ear-damaging : you can wear earplugs or maybe just the bass throbbing away will do the trick.
Thing 2: Learn from the masters.
Try listening to some motown or 60's pop/soul like Tina Turner, James Brown, Marvin Gaye, Creedence Clearwater Revival, Stevie Wonder. Also Janice Joplin. Pay attention to how they slide the notes about - especially sliding the pitch up to meet a note, and where they add vibrato in the voice. It's probably not contrived for these people - if they want to hit a certain note, it sounds like that when they do - but I think I can safely say that such soulful performers do so with style.
Thing 3: Strain a bit (but not much)
For most people, the tension in the voice gets more noticable as you reach the top of your range - or sing loudly- so that the voice gets a little gravelly. So try singing some songs where you have to try a bit to get the higher notes. Don't overdo it though as too much can damage your voice. Best bet is somethign that is generally comfortable but you have to stretch a bit now and then, either volume or pitch.
Thing 4: Don't apologise.
If you're going to sing, SING! Stand there and give it to them right between the ears. People want to hear it, so endow them in bucketfuls.
None of this relies on being able to sing accurately. Bob Geldof is a pretty flaky singer but gives plenty of emotion, as does Johnny Rotten (Sex Pistols). Or David Byrne (Talking Heads). There are plenty of examples like this- some of the 'emotion' comes from missing a note a bit or fluffing timing a little.
I hope you pick the guitar up again too !