Your dialogue is stiff because everyone is being too honest
Great dialogue can come from radical emotional honesty. But in most real conversations, people
dodge questions
answer indirectly
lie (badly)
change the subject
crack jokes to avoid serious answers
lie (convincingly)
say half of what they mean
tell the truth but get so anxious/angry/defensive others now think they're lying
If your dialogue feels unnatural, it might be because everyone is saying exactly what they think, or articulating their thoughts too well. Try letting characters hide things instead.
Subtext is where tension lives.
The best advice I ever got, and thusly, I think, the reason I always get compliments on my dialogue, is this:
Your two characters are having a conversation, but each one is having a different conversation. They should always reply to what they think the other person is saying, and they should always be wrong about their assumption.
Now, obviously, like any writing advice, this rule is meant to be broken. Any writing advice you are given is more like... a guideline.
