At the time, they were far more worried that the British would try to take them back than they were that the already several hundred year practice of slavery in America might continue awhile longer. In 1812 the British gave them good reason to fear being reabsorbed.
Also the slave states vastly outweighed the free states at that time. Had they chosen obstinance, they could have awaited the abolition of slavery in 1833 with the other British Subjects. No slavery, no Union.
Are you a History Professor? Best explanation I have ever heard on that era! Thanks.