Because you are filling out someone else’s ballot. You are voting for people that they may not necessarily have voted for. You are voting when they may not have necessarily (and by your statement, likely) have voted at all.
The ballot is supposed to be secret. You are violating that secrecy. The ballot is supposed to be up to the voter to decide, you are deciding for them.
As far as reasons to have such activities be illegal, I can think of several ways to use what you are doing for nefarious purpose.
I am sure that you are highly ethical, and would never do anything like this, but if I knew that you were voting for a dozen or so others, I might ask you to go ahead and mark all those ballots for my candidate or issue, and I’ll give you a bit of money, or some other compensation for that.
You don’t know that your neighbors actually appreciate your help. They may just let you fill in their ballot because they don’t want you to be upset with them.
If you were like “Hey, come on over on Thursday, I’ll fill out your ballot for you, then you can sign it and send it off.” Then refusing that offer may be more rude than they are comfortable with. You may be imposing without even knowing it.
If you neighbor says “Hey, fill out my ballot for me, but I do want to vote for ‘x’” then not only do they have to check to make sure that you voted for “x” rather than your preferred candidate, but you know that they voted for “x”, rather than your preferred candidate, and that may have an effect on whether or not they disagree with you on their own ballot.
I can think of a few more reasons why I think it is a terrible idea to be voting on someone else’s ballot, but that would take even longer to try to explain.
Let me know if you do not consider these reasons to be good enough to protect the integrity and secrecy of our ballot process, and I will try to explain more in depth. I have spent some time looking into seeing if your activity is legal or not, and while I think it leans toward illegal, based on the rules that you have to follow when assisting someone with a disability (which you are breaking), but if someone who actually knows or can cite the answer, it would be appreciated.
You have not answered whether or not you think it would or should be legal for your neighbor to give you the right to vote for him at the polling place on election day. Do you think that would be legal, if not, why would filling in the mail-in-ballot be any different? If you agree that it is illegal, do you think it should be?