Does the bike trainer kill the rear tire?

It wears it out faster, that's for sure.  it is a pain to change, maybe get a cheap second wheel (as if the sport were not expensive enough)...  but honestly I buy new tires every season, and I am sure the tire would last through a season of trainer and outdoor use, just keep an eye on the tread

My wife ruined her tire on the trainer.  Some people have no problems.  I am lazy and, thus, bought a dedicated rear wheel with a trainer tire to use only on the trainer.

Trainer tire - you'll get good at changing tires.

I did have a dedicated rear wheel for the trainer, but then got a PT so now I change tires twice a week.  I really only get one chance a week to ride outside.

It does for me.  Others who have the same trainer have reported differently.

I have a trainer specific tire on a old wheel I got from the LBS.  They made me promise to only use it on the trainer as the rim was damaged somehow and not suitable for the road unless rebuilt.

Kill, no, but it certainly provides more wear than riding on a smooth road with no potholes, glass or other debris. I wouldn't recommend taking a nice expensive tire on your trainer for 1500 miles on the trainer, then taking it to a race. I ride Michelin Krylions for races and training and have no issues. The jest is no, it won't kill it, but it will provide more wear on the tire than a typical ride. It is still very important to keep good tire pressure. Don't think just cause you are on a trainer you can ignore it.