What's wrong with this logic?

A real man would get married because he's not afraid of commitment. 

What's being wrong with this logic is that the person have an established belief and if reality refutes that belief the person distorts reality to fit the belief.

When the belief in the person's head is that "men (should) like commitment", and then finds that some men don't like to be committed, then instead of changing the belief, they change reality and claim that those men can't be real men, they're something else. This thinking resembles no true scotsman or moralistic fallacy .

Usually though it's just an expression of contempt for those individuals that do not comply with the standard (or stereotype) the person has or believes for a group of people. Instead of saying "I don't respect Y people who don't comply with my standard" they express it as "They don't deserve to be called Y".

It could also be a way to manipulate someone to do something by attacking the person's sense of identity, setting an emotional dilemma of choosing either to maintain their identity and do something they don't want to do, or abstain from doing it and lose a part of their identity. So it's a manipulation tactic. In that particular example there is also the loaded word "afraid" which makes a person look weak.
If the claim was expressed as
"A real man would get married because he likes commitment" -> Anyone who doesn't like commitment is not a real man.
that claim wouldn't be as strong as saying "afraid of commitment".
So the claim plays with the notion that men are fearless and weak men do not deserve to me called (real) men.
So, that makes that claim also an argument by emotive language 

The statement "A real man would get married because he's not afraid of commitment" is problematic for several reasons:

1. **False Dichotomy (or False Dilemma)**: This statement presents the issue as if there are only two options: either a man gets married to prove he is not afraid of commitment, or he is not a "real man" (implying he is afraid of commitment). This ignores many other possible reasons a man might choose not to get married, such as personal preferences, financial considerations, or a belief in different forms of commitment.

2. **No True Scotsman Fallacy**: The phrase "a real man" is a subjective and vaguely defined term. By saying that a "real man" would get married, it attempts to redefine the term to exclude those who do not conform to this behavior, thereby dismissing them as not being "real men."

3. **Stereotyping and Generational Bias**: The statement generalizes what it means to be a "real man," imposing societal norms and stereotypes that can be outdated or irrelevant. This fails to recognize that masculinity and individual choices are diverse and cannot be pigeonholed into one action or lifestyle choice.

4. **Overgeneralization**: The statement makes an overgeneralization by implying that marriage is the only form of commitment. Commitment can be shown in numerous ways beyond just marriage, such as in long-term relationships, partnerships, or through other personal responsibilities.

5. **Ad Hominem Potential**: Statements like these can lead to ad hominem attacks by belittling those who choose not to marry by questioning their manhood. This turns the discussion into a character attack rather than a reasoned argument about the nature of commitment.

6. **Circular Reasoning**: Implicit in this statement is a form of circular reasoning: it assumes that getting married is a brave or 'manly' thing to do without actually proving why marriage should be the definitive measure of commitment and courage.

In summary, the logic in the statement is flawed due to its reliance on false dilemmas, subjective definitions, stereotypes, and generalizations, making it an unsound and biased argument.