What do I do about this singer, do I just break the band up?

Yeah, gonna talk to the others.
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So evidently the guys in your trio don't care what you think. No working band I know would allow this to happen. Time to meet with your mates (without this singer, of course) and hash this out. Your input might change the situation, IF they care to listen. If they don't, and you are sure you don't want to be in the band with that singer, then you do what you need to do.

As others have said, here and all over Band Management ... COMMUNICATE.
 
I think I might have played with your singer before, but in my case he was a 6’7” drummer...

1. Get clear with guitar and drums - do you share a band vision that doesn’t include this guy? If not in alignment, find new band mates elsewhere.
2. If you all want the guy gone, tell him: “It’s not working w you”; “We just want to be a power trio for now (then look for the right singer and change you mind)” Anything that gets him gone. He hasn’t exhibited any courtesy so far, so maybe he’ll tell you what losers you are without him - that should make your job easier - nobody’s obligated to hang w a divisive jerk.
Otherwise +1 to what most others have said.
 
You need to clarify things with this "singer" and the rest of the band immediately.

I assume from your description that there's no band leader yet. Guess what? You're elected. And your first job is to communicate clearly to everyone that this guy is not part of the group.

Since he's been added to the group chat, I'd do it via the chat. It might save some drama at the rehearsal. You don't have to be rude, but you do have to be firm. Say something like "we (the band) have not yet had a chance to discuss what we are looking for in a singer, or whether we need a singer at all. I think inviting anyone new to attend any band meetings or rehearsals would be premature at this point. Thanks for your interest [singer], but we're going to have to ask you to be patient and understand that we're not open to new members at this time. If we decide to audition singers at some point down the road, we'll let you know."

I'd let the other members know ahead of time that you're going to send this message, so they understand where you're at and why.

Good luck.
 
You need to clarify things with this "singer" and the rest of the band immediately.

I assume from your description that there's no band leader yet. Guess what? You're elected. And your first job is to communicate clearly to everyone that this guy is not part of the group.

Since he's been added to the group chat, I'd do it via the chat. It might save some drama at the rehearsal. You don't have to be rude, but you do have to be firm. Say something like "we (the band) have not yet had a chance to discuss what we are looking for in a singer, or whether we need a singer at all. I think inviting anyone new to attend any band meetings or rehearsals would be premature at this point. Thanks for your interest [singer], but we're going to have to ask you to be patient and understand that we're not open to new members at this time. If we decide to audition singers at some point down the road, we'll let you know."

I'd let the other members know ahead of time that you're going to send this message, so they understand where you're at and why.

Good luck.
Well, no choice now. This kid trawled through the chat, found a message from THREE MONTHS AGO, where I described an incident where he dropped the lyrics and almost fought with the drummer. Now he's calling and texting nonstop
 
Well, I think this is taking an interesting turn. He literally trawled through months of group chats, found one where I said that he was a poor singer, and now he's calling me incessantly

Well, I’d say it’s pretty much resolved itself than at this point. If the other two are decent dudes, they won’t want crazy stalker guy in the group.
 
You need to clarify things with this "singer" and the rest of the band immediately.

I assume from your description that there's no band leader yet. Guess what? You're elected. And your first job is to communicate clearly to everyone that this guy is not part of the group.

Since he's been added to the group chat, I'd do it via the chat. It might save some drama at the rehearsal. You don't have to be rude, but you do have to be firm. Say something like "we (the band) have not yet had a chance to discuss what we are looking for in a singer, or whether we need a singer at all. I think inviting anyone new to attend any band meetings or rehearsals would be premature at this point. Thanks for your interest [singer], but we're going to have to ask you to be patient and understand that we're not open to new members at this time. If we decide to audition singers at some point down the road, we'll let you know."

I'd let the other members know ahead of time that you're going to send this message, so they understand where you're at and why.

Good luck.

Yeah, tell him all that stuff. Also,
" We have a 'No Insano Giants' rule"
 
I don't think you've listed any redeeming qualities of this "singer" (other than he's tall and intimidating -- maybe he can be your roadie?!), but just lousy personal and musical attributes. This seems like a no-brainer ...
 
So me and some ex-bandmates just assembled a three-piece. We are all talented guys I'd say, and we have the diversity of influences and the weirdness needed to make something unique. We basically have the know-how to make our own dream band, but there's one HUGE obstacle.

Ever since the "original band", there has been this... special guy who's had an interest in us. Way back when, during my dark ages as a guitarist I played a sort of "backing band" to this guy. He's a nice enough guy, but he's socially bizarre, and honestly can't carry a tune in a bucket.

I had to leave when he missed half the lyrics and did an off-key rendition of a Johnny Cash song, which even his brother called him out on. Basically, he's been badgering us to be his BACKING BAND (huge insult right there), and now wants in on our three piece.

My friends, not knowing the guy outside of facebook messages gave him the benefit of the doubt, and added him to our group. How do I fix this? I see great potential for us, but honestly, with this guy that potential is gonna be absolute zero.

Hell, even if we even get a show with this guy, he's prone to getting his band kicked off sets because he trash-talks other bands. Hell, he even trashed the drummer in THIS band, because I left his band to join this one.

I feel like this guy is gonna sink this band like a stone, and I wanna know if I, being the only songwriter, should pull the plug now, or try and reason with my bandmates.

Record early and often, and review. Secondly, find and prepare a new singer using the recordings to get him( or her) up to speed. Having him (or her) ready to drop in and gig will make this process of bouncing this guy a lot easier.