I almost never offer draws, weaker players may blunder and stonger players can provide a learning experience. My experience is that if someone doesn't offer you a draw they probably don't want one.
draw offer psychology
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If you're opponent offers a draw, take a moment and try to figure out why he thinks your position is better. (c) Nigel Short
I've only ever offered a draw twice OTB. Both in winning positions, one more clear cut than the other (although I didn't know it at the time). I was down to about 20 mins on the clock in both (which is nothing when you're as slow as me). One was accepted, the other wasn't and my flag fell when I was two pawns up in a rook ending
it is said the one rejecting a draw is often the person losing.
is it a true statement or have many burned their hands by rejecting a draw at some point in their chess life.
if people offer me draw I instantly think of this saying.
but accepting a draw should be based on a rational decision and not some more or less silly saying.
Bent Larsen said the reason many people lose after they rejected a draw. is that they think they have at least a draw in their backhand and therefore that draw offer became a pillow. So the player became a little reckless - thinking I have at least a draw.