It's an interesting subject, isn't it? I do think that people express their identity through the things that they own, the clothes that they wear and the way they conduct themselves.
If the gear truly doesn't matter to you other than to take the picture, then you would not advertise what you have. However people do advertise what they have in signatures and on their profiles. It could be linked with the idea of social status in the same way that cars are linked to social status. The better the kit then the more successful you have been in your life. There are not many people on minimum wage jobs with a £3000 lens, for example. It's Western human nature to want to show others how successful we are, to perhaps brag a little. Demonstrate that because we are good at bringing in money that makes us good husbands, fathers, friends, etc.
It is also part of a cultural tribe thing, in the same way that people become fanatical about Apple products, for example. 'Are you Canon or Nikon' is like asking 'are you my kind of person or not'. We exclude or include people based on the choices they make and the items they select. In the same way that we exclude or include people based on clothing, age, gender, etc etc.