MawBroon, I'm sure that you would wash up your cup carefully, wrap it up and, when you fancied a cup of coffee when you are out shopping, hand it over safely to a barista to have it filled. But not everyone is like you. You could follow someone who has brought back his/her disposable cup from a couple of hours earlier (cup with no handle, possibly not even washed or swilled out in a washroom), barista busy and grabs the cup in hurry, puts her fingers on contaminated parts, fills cup touching the coffeee making equipment as part of the process, passes cup back and picks up yours. Imagine a busy coffee bar and think how often this may happen. It's introducing contamination which wasn't part of the process before.
Some are saying I'm paranoid but I think providing your own cup to get a discount to drink out (off the premises) is a poor solution to the problem of not being able to currently recycle disposable coffee cups.