I often come across people saying to each other:
I don't want to be too dense here, but…
What does the term dense imply in such contexts?
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Someone who learns something slowly is said to be "dense". It seems related to the expression "thick-headed", where the conceit is that thoughts don't travel quickly through someone's head to be retained if they have a thick head. This kind of "density" also seems to imply slow transit of information into a person's centers of recognition.
Another expression that has nearly the same meaning as dense is "slow on the uptake". When used as you quoted it, the speakers are likely apologizing for their own slowness at getting the gist of an idea or argument.