Because as we're now seeing, people can actually be easily fooled into making illogical decisions that are not in their economic interest.
I agree that such comments could backfire and increase negative sentiment toward the EU - but taken at face value they do offer an incentive for populations of other countries not to follow the same route.
And that's exactly what is happening, every comment or snipe the EU makes towards making Brexit painful for us simply re-enforces the position that they simply refuse to listen, refuse to learn and refuse to change.
Making Brexit a "harsh deal" to make "an example" just shows what sort of institution you are dealing with. The fact they have to resort to make such threats/comments shows they are running scared. A country should not be held to economic ransom by the EU if they think they can do a better job without it. Instead the EU should be putting forward strong, reasoned deep hitting arguments to the UK on all the good things they offer us. But they do not, they sit on their laurels and simply focus on the negatives, re-enforcing them with more negative dialogue. No wonder people despise it. Just look at the last presidential elections in the US? "Yes we can" and "Lets make america great again". Positive messages.
All we got from the ******** group was negatives. The leavers gave people the hope of something better. When a group shouting the grass is greener can outshout the status-quo group because they can't put forward equally compelling arguments for the status-quo you know something is stagnant and wrong. Where were the positive messages from remain? Where were the big projects, and the messages of better things?
The only legitimate concern the EU has is that the UK may in fact do better outside the EU, and honestly, given how countries and pre-negotiations are already lining up to set up deals with the UK, who can blame them? They are so concerned by this that this is why they have resorted to playing hard ball, because if we do make a good go of it, others may join us and the Brussels gravy train will be over.
That is what the EU is scared of.
At the end of the day, you can put forward all the economic and scientific arguments you want, but the message needs to speak to the heart of the electorate to win. A fact, certainly lost on many many remainers.