Earlier quoted context omitted.
"And your Father, who sees what is done in secret, will reward you." So still selfish (if doing it for the reward), but that is human nature.
"do not let your left hand know what your right hand is doing"
The reason I think that, is because in ancient Roman times they had a way of counting on your fingers where you could count up to 100 on your left hand alone (then you could use your right hand after that for even larger values). [1]. So if the context is "small values" and charitable giving, it makes more sense to me at least.