I always read that using the same password on multiple sites is a risk. I'm wondering what is the real reason for this?

In my case, I use the same password on multiple sites everywhere. My password is, however, very strong and complicated and long that I saved in a text file and then copy for each connection on sites to which I subscribe. Does this method protect me from the risk because my password is too complicated and long?

Password reuse is a security bad practice because of of a simple attack scenario like this one:

Source: XKCD
With reusing a long and complicated password, you are still facing the same threats as highlighted in the above schema.
In addition to this, saving a password in a text file is an unsafe practice in that the privacy of your password depends also on the safety of your computer (think of malicious browser plugins you may install, drive-by download attacks installing spyware on your machine ...) and that of your network. You may also consider other scenarios like with phishing attacks on which the strength of your password does not play a role.
