"Privacy loves company."
The key is to understand why a coinjoin transaction provides privacy. It is not a magical veil that shields your financial history, it is just a tool that helps obfuscate a particular output's history. This obfuscation is only achieved by including many inputs in the coinjoin transaction, such that each input could be the source of a specific output, but it is not technically possible to determine which is which.
With this in mind, we can see why having many participants is important: you want to have as widely varied a selection of inputs as possible, so that your output's history is not meaningfully determinable. If you only include your own inputs, then each and every input will have a history that leads to you.
To illustrate this point, consider the case in which a chain analysis firm has a very good idea of who owns each UTXO that exists:
If you supply 10 inputs to a transaction, but a chain analysis firm has linked your ID to those 10 inputs, then it would be trivial to determine that you likely own the outputs created as well.
On the other hand, if you supply 1 of 10 inputs, then the chain analysis firm would be hard pressed to determine who owns each newly created output. With no additional info, there is just a 10% chance that you own any one specific output.