First off, “psalm” doesn’t mean “song.” In Greek, it means, “a striking” and refers to plucked musical instruments - specifically, the psalterion.
The Hebrew name for the Book of Psalms, “Tehillim,” does mean “praises, songs, songs of praise.” Each individual section of the Tehillim is called a “mizmor,” which means “melody, tune.” It is particularly associated with songs sung with a harp, as with David in the Bible. (Hence the Greek name for the Psalms.)
Second, there is a place for the silent Mass. It is not as desirable, but it’s more desirable in many ways than a messed up musical Mass.
Now, where to start?
We sing as an offering to God of prayer and praise, a physical act which resembles incense rising to heaven, and which imitates the angels and saints in Heaven. God specifically commanded that the Levites sing to Him, and it has always been the practice of normal Jewish and Christian people from the earliest times to sing praise to God, to beg His help in song, and to thank Him that way also.
As with a lot of other Church practices, in our own time we find confused teaching by members of the Church about music, singing, the responsibilities of the congregation, and so on. Frankly, most of that stuff ceases to be confusing if you go back to the older documents and practices. But not entirely, because there have always been a lot of situational decisions about music, and you have to understand the situation to understand the local decisions.