Doctors make a big deal out of it because of history - forced or unwanted sterilization has been a problem in the past, especially for marginalized people. The difference between men and women's experiences are infuriating and MUST be addressed, but the sentiment is correct.
A successful vasectomy ends in a 50-50 reversal-to-conception ratio, including not just pregnancy via intercourse but by any means necessary (fertility treatments, IVF, etc.). Even this minimally-invasive and "easily-reversible" action is considered permanent. Any permanent sterilization (in CA, not sure about rest of US/world) has a default 30-day waiting period, with the ability to waive down to a minimum 72-hour required delay between consent to permanent sterilization and having the procedure.
Making a permanent decision is not something to be taken lightly, it will be interesting to see what other outcomes of Roe v. Wade change behavior and expectations of large populations.