Explain why it is impossible for a man to be a carrier of a sex-linked trait.

Because it contains two different sex chromosomes

Explanation:

Man in its genome contains two sex chromosomes, X and Y, while woman contains two X chromosomes.

In order to be a carrier of a sex-linked trait, a person should have one copy (one allele) of a certain trait. For example, if a female has one X chromosome with mutation (e.g. disease carrying) and one normal X chromosome, she is carrier for the disease. But, on the other hand if a male has one X chromosome with mutation he will develop that disease.