I've been Mrs Mymaidenname for the 15+ years I've been married. Why on earth can't I be a Mrs if I haven't taken his name?
The way it was explained to me is that 'Mrs. Smith' means married to Mr. Smith. If you continue to use your maiden name of Jones, as you are not married to Mr. Jones, you cannot be Mrs. Jones, only Ms. or Miss.
Personally, I don't care - it should be up to the individual woman. The two women I know best who haven't changed their names professionally, both use their husband's name in their personal life. One uses Ms. Maidenname at work and the other is a medical doctor and therefore the issue doesn't apply, as she is addressed as Dr. Maidenname.
It was explained to you wrong.

Mrs is the female head of household.
Now the thing is, in past times women alone could not be a head of household, she would have to marry to become so. (For example even as recently as the 1930's when my grandmother graduated college and moved to NY to become a nurse she could not live in her own apartment. The hospital
required unmarried staff to live with their parents to in dormitories. Being her own head of household in a small apartment was not allowed even though she had a degree and financially supported herself! And that was an enlightened time when women could get educations and jobs and even vote - but they couldn't be heads of household.) So therefore in that political/legal sense one could only be "Mrs" if one was married. But that was a technicality, a default, not the end all. The end all of Mrs is "mistress" as in the mistress (head of) the household. Technically, grammatically, any woman who supports herself is a Mrs - so once you move out of your parents home and start paying your own bills you are a "Mrs" marriage not withstanding.
Common usage =/= only proper usage.