Five reasons why to learn intervals:
1) After some interval training, you don't have to think any more about what interval it is, you simply know. You have internalized it and recognize instantly without thinking.
2) You will hear tunes and harmonies more clearly. Since you have become more aware of intervals you start hearing notes more in groups and structures.
What first sounded to you like like a bunch of notes jumbled together you will now hear as individual notes.
You can still enjoy the overall effect of the music like anybody who knows nothing about music but you will be able to hear more in detail and you will understand what exactly is actually happening. You will, for example, be able to identify a major triad chord. This knowledge is important for being able to play by ear or for writing music.
3) It will help to learn sight-reading. It is easy enough to see whether a note goes one or two steps up or down but once there are bigger intervals involved it can get challenging.
4) It brings music theory to life! Rather than just recognizing a major third or a perfect fifth it reveals that a major third has a certain characteristic and that a perfect fifth has a certain quality. That applies to chords as well as intervals.
5) Become comfortable and reassured in playing music. Being aurally trained makes learning new music easier, gives you confidence in playing by memory, improves your sight-reading, helps you improvising and gives you a better understanding of the composition.