My husband always argues with my family

We got married five years ago. My husband is eight years older than me and is generally a mature man. He completed his psychological doctorate degree overseas after studying abroad since he was in middle school. Both of his parents are professors at universities.

Meanwhile, I come from a normal family background, with my parents running moderate businesses.

I have a feeling that my husband overtly likes to argue and to show off his knowledge while looking down on others. I was taken aback when I discovered that, since I did not think he was that kind of man before marriage, and he appeared humble, as well as willing to listen to others’ ideas, when I first brought him to introduce to my parents.

There was this one occasion when my husband argued with my brother over a topic relating to education. It took them two hours to argue back and forth, to find proof supporting their ideas, and to protect their own reasoning. Starting off as a normal conversation, the talk then escalated to a fierce argument, which made my brother mad and my parents annoyed.

My husband told me that my brother was stubborn after we got home. He said my brother had a close mind as he was still unmarried and stayed with my parents.

When I suggested to my husband that he should probably behave more carefully, he got mad and replied that he just wanted to "train" my family’s ability to critically argue. He said he did so for my family’s sake, and stated that he would never visit my parents again.

What should I do to ease the relationship between my husband and my family?