I agree that Cousin It's statement is literally false due to his use of the word all, but given that not all men are perfectly mature in your sense, I expect the essential concern to remain valid: adding a woman to a male-only group will tend to change the social dynamics, in part due to the impulse that Cousin It mentions.

(I mention this for the sake of completeness; speaking only for myself, I think that explicitly single-sex groups are a terrible idea and would not participate in one.)