My experience.

I tried to learn to sing harmony and gave it up for a number of reasons.
I learned, the hard way, that the problem is not singing harmony, it is creating a harmony.
I was able to create simple harmonies while sitting at the piano but it was a long and laborious process. I then had to memorize the harmony and hope that I could remember it when it came time to sing it. Sometimes yes, sometime no.
I never got to the point where I could create a harmony on the fly.
I finally gave up.
Be gentle with your fellow singers.

Russ (Permanent GUEST and melody singer).