Mr. is a contraction of the word Master, which despite its other uses in this case simply means an adult male, either married or not. At some point unknown to me, there was a split between Master and Mr., where Master came to refer to a young unmarried male and Mr. an adult. Mrs., similarly, has its origin in the word Mistress, which again once meant an adult female, married or not. At some point in the 17th century--so a cursory glance at Wikipedia tells me--the term for female adults was broken up into Miss (unmarried woman) and Mrs. (married woman, any age), and later Ms. (generic term for when marital status is unknown). These are the simple facts, and anyone with an even cursory knowledge of etymology should either know them or know to look for the link before endorsing such an obviously facile argument as "Mrs. looks a whole lot like Mr.’s." This of course leads to the question of why this meme got started and, more importantly, spread.
Just looking at it, the "Mrs./Mr.’s" meme smacks of the same sort of faux-consciousness-raising reasoning as the foolish "history/herstory" meme from years ago. Even if the "Mrs./Mr.’s" meme was originally born out of honest ignorance, I suspect that consciousness raising played a part in its spread, as I've seen otherwise knowledgeable individuals passing it around.
The problem with this sort of thinking (that is to say, the "it draws attention to a problem even if it isn't entirely correct itself" thinking) is that it makes your whole argument look bad. This is the sort of thing that, when disproven, tars any further arguments you want to make with an air of unbelievability, because, in the most generous light, it sounds glib. And if your argument comes across as sincere, then it sounds ignorant. Neither of these are good for your cause, especially when a meme like this spreads widely across social media, because it undermines the credibility of everyone who agrees with you, not just yourself. Your entire side of the argument becomes "those people who endorsed that silly meme with no factual basis" instead of "those people who have valid, thought-out arguments that should be listened to."
Perhaps the most frustrating thing about this (and, really, why this post is so long) is that there are good arguments to be had on this subject that are legitimate and thought-provoking on their own. You don't need this kind of afactual bullshit to get the point across. There should be real discussions about the fact that we cling to an outmoded form of titular address that classes women based on their marital status and men on their gender and entirely ignores the advances made in gender equality, not to mention the fact that it entirely snubs the transgendered. Frankly, if we want to acknowledge age with a title at all, it should be either genderless or take into account the myriad of genders that actually exist, not just the old gender=sex1 paradigm that is being phased out (no matter how much some might wish otherwise).
1 This refers to... shall we say, ’basic’ sex as opposed to genetic sex, which is quite a bit more complicated.