You stop seeing their pictures
The biggest disadvantage you might face is that you would stop seeing their pictures in your feed. If you wish to see their photos and stories, then you would have to follow them again. But, if their account is not private and public, you would still be able to see their pictures and other updates.
They still see your posts
People you unfollow would always check all your updates and pictures provided that they are still following you.
They won’t get notified
The best thing about Instagram is that if you unfollow someone, they will not notify that. But, if you start following them again, then they would get a notification for that.
Their follower count would get decreased
If you unfollow anyone on Instagram, one significant consequence is that their follower’s count gets lessened. Many people keep a count on their followers; if they see that the followers got reduced, they might conclude that someone might have unfollowed them.
You will disappear from their follower’s list
If you unfollow someone on Instagram, then you automatically get removed from their follower’s list. When they would check their list, they would not be able to find you. In that case, they would get to know that you unfollowed them. (See What happens when you block someone on Instagram?)
They can still message you
The person that you unfollowed would still be able to message you. As the messaging process does not gets altered by the unfollow thing.
You might have to request authorization again
There can be a situation when you unfollow someone once and then choose to follow them back. In that case, you would have to wait for the person’s approval if their account is private. (See what happens when you unfollow someone on Facebook)
Your likes won’t disappear
The good part is that your likes and comments would not get removed if you unfollow someone. All the like and comments would remain intact whether thou follow or unfollow anyone.
Why your profile picture doesn't get a lot of likes on Facebook | Why some people don't like my profile picture on Facebook?
Why do girls make their Instagram private? Why do some people switch their Instagram account from public to private?