Filling out forms that ask for “relationship with”

Think of the question being asked as "relationship with son"—does that help to clarify it?

Your relationship with your son is "father."

His relationship with you is "son."

They're asking for the first, not the second.

Forgive me for being perhaps nitpicky here, but my guess is that those forms you fill for your son really mean "relationship to child" not "relationship with child". Your relationship to the child would refer to how you were related to him/her, e.g. guardian, father, mother, uncle, etc, while your relationship with the child would indicate how well you get along. This distinction is debatable, though, and it is obviously inconsequential in a form such as those you fill, where the intended meaning is clear.

That being out the way, the correct response, assuming you are the father, should be simply "father", since the question is directed at the person filling the form. On the other hand, if the question began thus: "Child's relationship to person filling the form", or something along those lines, then the correct response in your case would be "son". While "father-son" may take care of any perceived ambiguities in the prompt, it is information overkill in this context and would only be most appropriate in response to a prompt such as the following: "Relationship between [your son's name] and person filling the form".

Also, if you are worried because it says "child", I am sure another section of the form indicates your son's gender. Creators of such forms clearly have to use "child", since the forms will be used for or by both sexes, except in the case of a single-sex institution.