Captain Archer had previously been stuck in some kind of quantum tachyon loop and with holographic inversion so he had to present himself in the appropriate attire for the era.
Probaby s3e12 "8-1/2 Months" where he leaps into a late term pregnant woman.
Think this is the segment:
"Come on, this is the '50s. What high-school kid is gonna be able to pay for a baby? If you think I'm going about this wrong, give me a better idea, or better yet, ask Billy Jean. But not the terrified 16-year-old in the waiting room. Find Billy Jean, the woman. The one who spent her whole life looking for her only child, and ask her what she wants me to do."