The statement that the seasons are wrong, does not make sense. To tie these names to a calendar, does not make sense.
As a trivial example, a couple of weeks ago a local newspaper reprinted its usual "What's on in London in April?" article, and one of the items was "the first half of April is peak cherry blossom season".
Er, not any more it isn't! Most fruit trees were already in leaf by the time the paper went to press, with only a few prunes remaining with significant amounts of blossom. And we'll see a similar article in May talking about bluebells, despite them actually being at their peak right now. So that's a shift of 2-3 weeks over the course of the two decades that that particular publication has existed.
And it might not matter so much if the seasons were changing equally for all species - but some instead rely on day length, yet others on the amount of sunlight (which has been low so far this year). So pollinators are arriving only at the end of pollen season, predatory insects are finding their prey diminished by starvation, rodents haven't hibernated, and entire ecosystems are becoming weirdly distorted.
Australia calls December "summer". If climate patterns changed and shifted our weather patterns by a month, we'd shift our season vernacular to match.
Seasons refer to the climate we experience. They're a human experience, not calendar slot.