The purpose, I find, of these motivational flourishes you speak of are quite simply to shame people and simultaneously inflate one's own ego.
You can take this very same "meme" and apply it to school or finances like Opiate has maintained for a few pages and others have been saying since the beginning in order to further contextualize the condescending nature of the question. To even frame not being in shape as something that needs to be excused is aggressive in the first place.
Would "why should I have to?" be a valid response?
That the meme frames "not being in shape as something that needs to be excused" is your interpretation. I see it as a response to the prevalence of excuses that are trotted out by people when explaining why they won't take the steps of engaging in diet or exercise in the first place. Obviously if you're not making excuses to begin with it doesn't apply, but many people do so. Whether it is an effective challenger of those excuses or whether it turns people away is up for debate; judging by this thread I'd lean towards the latter.
As for Opiate's examples, they were silly. The basic point that people have different contexts influencing their achievements is valid, but the specifics were not comparable. If you think the barriers to entry and amount of time, effort and even natural predisposition required to obtain a degree from a prestigious university are comparable to those required to engage in a basic physical training program you're either ill-informed or being dishonest. But Opiate's examples fail at an even earlier hurdle: he is comparing outcomes to processes. These memes (by and large) don't contain pictures of Olympic medallists or models or bodybuilders and then ask people why they haven't reached a similar level of achievement, they show people with a large disadvantage making an effort. The (purported) 102 year old on the rowing machine isn't going to win Mr. Olympia, but he is applauded for not letting excuses dissuade him. The woman in the OP isn't saying "I've had kids too so why don't you look as good as me?", she's saying "Despite having children I make time to exercise." Her appearance is simply a visual heuristic for confirming this. It may be an attention grabbing and obnoxious one, but that's all it is.
If you take a look at the fitness thread on this very forum (and many others like it), you'll find that most people don't care if you're fat or weak or skinny or slow, they care if you have a positive attitude and are willing to learn. When people say things like "I don't have 20 hours a week to spend lifting weights" it demonstrates that they are unwilling to put even the slightest effort into researching the topic and thus are "making excuses". It certainly doesn't help that vast swathes of the fitness industry peddle FUD aimed at confusing customers, distorting their body images and hampering their efforts to improve their health in order to prime them for continued consumption, but lashing out any time you're told that you've been sold a lie is a good way to ensure that you'll keep making excuses and that any effort you do make will likely be in vain.