I envision singing melody with left hand piano and right hand stabs, arps, or something.
Hi Bernie, that's what I thought you meant. I know lots of trained pianists (keyboardist) who have that problem. I think the reason is that, unless you're studying jazz or are essentially self-taught, it's just a part of formal music instruction that's NOT TAUGHT. For a lot of musicians, it just comes naturally; they sing a phrase and just 'hear' a 'comp' phrase that would compliment or accent it. Hard, but not impossible, to learn at a late stage in your musical career. I could only suggest two things:
1. Get a musician that is skilled at this to show you a few 'tricks'.
2. Find some commercial arrangements that incorporate what you envision, and listen, study, and practice what they're doing.
It'll take some time but once you discover the technique, practice, practice, practice until is feels 'natural' and almost unconscious.
chas