Thank you for your question. First, a gentle reminder, “an” is used before a vowel. You would use “a” not “an” before disappointment. The answer to your question would depend on the speaker. If the father was the speaker (or writer in an email or letter, for example), he would be saying that he tried to teach his son. The father believes that fathers are supposed to do so but his son turned out to be a disappointment. If the son were the speaker (or writer), the reverse would be true, it would be his father who failed him. I think you meant to say “failed you.” Not “failed with you.” Failed with you would have an entirely different meaning. It would mean that both parties failed together.

The father is disappointed by his son and is disappointed in himself for not teaching his son better. (It's a form of accepting part of the blame)

didn't succeed or not successful.

The "with" refers to comparison with others. With the first two children, I did ok, but for some reason I failed with you.

Failed somebody means let somebody down. the father failed to teaching his son about life