Then you are not listening to very cogent lyrical music. I'll admit the lyrics are not always the first thing I notice and sometimes I'll be listening to a song regularly for months or even years before I notice words that flip the meaning of the song in its head, but i generally find weak lyrics almost always belie a weak song.

Additionally being raised on classical music is not necessarily a good way to be raised on music as it's a very limited genre that has not progressed for 200 years. 95% of the greatest classical musical was written before 1827, and music since evolved to things like Opera and folk (Beethoven's late strings were his attempt to move music passed the classical era). Post 1827 classical music generally is concerned with technical arrangements that while being impressively difficult to play, have limited emotional range. In some ways very similar to much metal music, which often claims late romantic era composers as influences. Camille Saint Saens advocated for as much at the time, though he was actually a bit of an exception since he at listed acknowledged the lack of classical musical direction following the death of its final great composer.