Perhaps, that particular post in isolation.
My comment was more based on the fact this gets peddled out all the time. The faux outrage that "Sue" whilst waiting for a lift, makes small talk and has commented that she's tired, to "Jane" an acquaintance who happens to have kids. Now, the reality is, Jane doesn't really care, it's just small talk, and makes a throwaway comment like "Ugh, don't. You should try a toddler and a teething baby who wakes up every hour, ha ha." Jane isn't in competition. It's just a turn of phrase. Jane is doing that typically British thing of agreeing with a moan, by applying her own circumstance. And Sue knows this really.
But. Sue can't miss the opportunity to try and twist this into "oh such an obvious derogatory comment to the child free, like myself." It's all so deliberate.
I think in general, child free women get a raw deal. People who can not fathom their choices, belittle their choices, and that's so wrong. But it doesn't help when a minority try and twist absolutely anything into an attack on them. It just dilutes the credibility of the group they represent.