It's quite understood among many people how the phrase "it's not that deep" reflects a rise of anti-intellectualism. I've seen various apt descriptions of it, from "anti-anything-deep" to how it's a thought-terminating cliche that shuts down critical thought and prioritizes vibes over knowledge.
That's fine and all, but I want to focus on a particular facet of what it implies: that there is even a single extent of appropriate depth for any given topic or problem.
It's less abstract than it sounds. Multiple distinct levels of analysis, distinct mutually non-exclusive framing and perspectives can pertain to the same topic. Distinct arguments can validate/invalidate the same conclusion. Not all of them will exhibit the same level of depth by any meaningful measure of "depth". Yet, they all pertain to the same topic.
As an example, there can be multiple ways to approach some silly social media take like "Godel's incompleteness theorem is why rationalism bad and postmodernism good".
Explain how a highly narrow and technical theorem about certain formal systems, a scope-mutilated vibes-based version of which has spread through osmosis on social media, cannot be used to make grand conclusions about epistemology.
Instead of engaging directly with the "argument" made, consider how it reflects pseudo-intellectualism, over-confidence in "inferences" based on superficial pattern-matching, and how it's an example of a broader pattern.
Instead of directly referring to the preconditions of the theorem, consider the nature of how grandiose the claim seems, and other contextual clues like what else they post (e.g. is it the "quantum quantum quantum is why divine feminine energy" kind of poster?), how they respond to people disagreeing with them and whether they follow common patterns of being an internet grifter, etc.
I could go on with examples. Any of these lenses is not necessary "deeper" than another. In a way, they're entirely different and can't even be compared on the same axis. The first one is about highlighting the logical flaw, the second one is about broader social patterns, the third is about assessing credibility. They also don't necessarily contradict each other. One could do all three.
So really, the phrase "it's not that deep" does more than just being a thought-terminating cliche that presents a shallower engagement as more appropriate without substantiation. It also implicitly presents a narrow frame, perspective or lens as the only reasonable one. The users of the phrase typically have already decided on a certain framing as the default and the only valid one, and even anything that is not exactly "deeper" but different gets the "it's not that deep".
Usually, those different frames are the ones that the phrase-user is unfamiliar with or those that lead to conclusions that they may disagree with. Sometimes, what is merely unknown and not obvious can seem deep. Mostly, it's more of a rhetorical tool rather than being a genuine assessment of whether extended depth given any specific kind of analysis would have diminishing returns.
It tells you more than just to think less. It tells you to think a certain way.