No, it is not common for men (or women) to want their girlfriend (or boyfriend) to meet their parents on the first date. Introducing a romantic partner to parents is typically considered a significant step in a relationship and is usually reserved for later stages of dating when both individuals have established a deeper connection and commitment.
On the first date, people are usually getting to know each other and gauging their compatibility and interest in one another. It's a time for casual conversation and getting a sense of each other's personalities and interests. Meeting parents would be considered too early and might be overwhelming for both the person being introduced and the parents themselves.
Introducing a partner to parents is generally done when the relationship has progressed to a more serious stage, and both individuals feel comfortable and ready to take that step. The timing of such introductions varies from relationship to relationship and can depend on cultural, personal, and other factors.
If someone is suggesting to meet their parents on the first date, it could be an unusual or uncommon situation. It's essential for both individuals to communicate their boundaries and expectations about the pace of the relationship to ensure they are on the same page.