What is the difference between "dispute" and "argue"?

There were two English teachers who told me different answers. I'm confused. When I want to talk about two persons having different opinions, I have to say that "they dispute with each other" or "they argue with each other." One of my teachers said we didn't use dispute with people, but we use this word for politics and law. Another teacher gave me the following examples while we are learning the S.A.T. word dispute:

• They got into a dispute over the phone bill.
• She will dispute any suggestion you make, because she doesn't like you.

Are the teachers right? Can I use dispute when I want to talk about people?

Solution 1:

Both the teachers are correct, in different situations. You cannot dispute with someone, but you can get into a dispute with them, or you can argue with them.

Bob disputed with Sally over the phone bill. (Incorrect)

Bob argued with Sally over the phone bill. (Correct)

Bob and Sally got into a dispute over the phone bill. (Correct)

You can use dispute as a verb when you're talking about inanimate objects (including but not limited to law or politics), but it doesn't make sense to use when the object is another person.

Bob disputed the false charges on his phone bill. (Correct)

Bob disputed Sally about the dinner plans. (Incorrect)

Last but not least, there are cases where it may look like the object is a person, but really it's a person's idea or position (ideas being inanimate objects).

Bob disputed Sally's belief that the Earth was flat. (Correct)

Solution 2:

All of the following are correct:

Bob disputed with Sally about/over the phone bill.
Bob argued with Sally over the phone bill.
Bob disputed the phone bill.
Bob argued with Sally about/over the phone bill.
Bob and Sally were at variance about the phone bill.
Bob and Sally had discrepant ideas about the phone bill.
Bob contested the phone bill.
Bob and Sally were at odds about/over the phone bill.
Bob and Sally disagreed about the phone bill.