I presume this is a condition called Duanes retraction syndrome in which there is simultaneous innervation of both eye muscles which is responsible for moving the eye to the left(medial and lateral rectus muscles)before birth. Compare that with a light switch which switches fan as well. When you do look to the left, your left eye closes partly as well. Ask somebody to look at you when you look to the left.
Imagine when you are flexing your arm, your biceps muscle contracts but at the same time your triceps muscle has to relax. If it did not relax, your arm will remain straight in other words you will not be able to flex your arm. This is a similar situation with your left eye in which your medial rectus muscle has to relax to allow your lateral rectus muscle to work or contract. You should not get it operated on for this. There is an operation for this but the outcome is not very satisfactory. Moreover it does not cause any problem apart from cosmetic affect. See a squint surgeon if you want an operation.