I too was once a squeezer and quickly discontinued the technique because of what many brewers have learned about this practice; better beer is brewed by avoiding the squeeze. The two primary compounds that are extracted from malt during mashing and steeping are soluble carbohydrates and proteins. During exposure to hot water, some of the soluble proteins precipitate. In brewing lingo this is trub. When grains are used in a mash, most of the trub precipitated during the mash remains in the spent grain bed. Most brewers who mash recirculate the wort back into the mash until clarity is achieved. The reason this is required is that it takes some time for the mash bed to set up as a filter. Once clarity is achieved, clear wort is run to the kettle.
When specialty malts are steeped in a grain bag the grains really do not behave as a filter and trub is not filtered from the wort, as is the case when a mash tun or lauter tun is used to separate spent grains from wort. Nonetheless, some of the trub is retained in the grain bag. By squeezing the grain bag more trub and cloudy wort is moved into the wort. This is why gently rinsing the bag with hot water is suggested instead of squeezing; it also extracts more of the good stuff from the grain bag.
An argument could also be made that squeezing the grain bag may also extract more polyphenols from the specialty malts. I am not sure that this actually happens, but it is another reason not to squeeze the bag. You can also end up with some small malt particles in the wort if your mechanical method is too aggressive.