1) To keep yourself separate from ideas. If they are yours, they are harder to change. Paul Graham spoke about a similar idea in an essay about keeping your identity small.
2) It helps remember them, and create a system you can iterate through. Like, "are there any ideas from economics which are helpful here?" and so on. This is an idea from Charlie Munger.
3) It lets you avoid sounding like a fraud. If I say "I have this idea that you need to practice for 10,000 hours to get good at things", or "I came up with a theory that the force applied divided by the mass will give me the acceleration", I sound like a fraud. To function in society you need people to not think you are a fraud.