Short Answer: You can't.
What they're asking for isn't difficult. Just throw the <br> tags back in and call it a day. If he complains about it being ugly, tell him it's because line breaks defeat the purpose of being responsive.
You can lead a horse to water, but you can't make it drink. If your client wants the stupid line breaks and he's signing your checks, give him the line breaks. If you've made your case, at the end of the day you can at least say "I told you so."
As a developer, I do things all the time I know aren't the best way, and knowing full-well I'll have to go back in and correct it... all because the PM/Client thought he knew more than I did.
But, at the end of the day, people are gonna believe whatever they want. If you're a doctor who doesn't beleive in acupuncture, and your patient demands to be treated with acupuncture, then perhaps they would be better off dealing with an acupuncturist. Otherwise, either you're gonna do something you perceive as a waste of time, or the customer isn't gonna get his way.