Can you want both praise and degradation?

Yes, and it's more common than either camp tends to admit. People contain both, and which one lands depends on the person, the mood and the day.

The shorthand the community uses is praise kink versus degradation kink, and treating them as opposing teams causes people to under-report what they actually want.

The practical consequence is that this needs negotiating per scene rather than per person. "Which one tonight" is a reasonable question to ask someone you know well.