Logic here refers to the logical steps you think your music should take because they sound right and that's what you know and believe. When you follow where the music should progress, it doesn't leap off someone's iPod.
Me writing a fake instrumental song where we have three repetitive verse-chorus things going on. The first time, you have it go as is. The second verse-chorus, alter that main line so it's not the same. Or add something in the background. Two new background threads! On the final round, follow the path halfway and write for whatever you're feeling.
You could be mad and weave that into the song structure by turning something into an octave jumping minor note series on the lead instead of C-A-C-D. This is the point where people cross into expressing themselves or being one of many on social media with basic songs they never took further. I'd go as far as saying this itself is where music separates from math and science in its creative point. Very few people jump off the cliff into the ocean here. You need to do so with your music. Stop the logical flow of where you think a note sounds good.
Take your hand off that whole section of keyboard and lay it elsewhere. Hit a key you feel is wrong. Does it sound wrong? Try the next one. Another. Oh, see, the third wrong note is a right. And it inspires you to do the rest of the song differently! Now you've discovered the note that has this whole alternate universe melody best friend to the original melody.
Whereas! Your original song would've been da duh da duh da duh the whole way through. See the change? Your song is no longer about math forming sounds. You've done something nobody else has in this world with your material. This, friends, is how you make cover songs original. Be bad like Darth Vader.