Once again, you've just told us you wish to remain in the EU, we get that, now just answer the question of why free movement and free trade need be intertwined. Having asked you a question about why the EU would wish to 'punish' the UK at the WTO about two dozen times without receiving an answer, I'm not really expecting you to answer this new one either.....
There's absolutely no reason why free movement and free trade have to be intertwined in an abstract sense. However what we know is that the EU have publically said they won't grant one without the other. In fairness this has not been an idle threat and both Norway & Switzerland have had to sign up to both to have access to the single market. Maybe May/Johnson/Fox can pull off an amazing deal for us by securing one without the other but it would be reasonable to accept that presently in terms of what the EU are offering they are closely intertwined?
As for the second question I'm not sure why they would want to punish the UK at the WTO particularly if we were in a trading bloc with them. It would go against their interests. They may wan to do so to be vindictive, but once you get past the rhetoric it's rare decisions of such nature are motivated centrally by vindictiveness but rather self interest.
The reality is that the it is not in the EU's interests to allow one without the other. Their aim is to make the EU the strongest trading bloc possible. Put simply free movement of capital and goods will benefit the wealthier countries while free movement of labour the poorer country's.
As a slight aside I do understand people's concerns about immigration. In many ways I agree with aspects of it but probably think people are putting short term needs ahead of a longer term picture. I am also not a member of the metropolitan elite (how I wish I was!). I have lost a job to a migrant and have worked for companies that were founded by migrants. I have also taught children from a variety of immigrant backgrounds (one class I taught had 7 languages spoken, so there was never a dull day in that job!)
My overall impression is that while there are negatives and lots of people lose out and have lost out there are also positives. Those benefits have not been spread out evenly and have re-enforced already uneven development across the country. What I do regret is that a sensible debate hasn't been had, but rather a caricature of one side only presenting the negatives and attacking anyone who tries to add some balance. Unfortunately politicians increasingly across the spectrum have joined in with this. Overall I do think this has not helped resolve the issue, as it's become a polarised debate with one side giving just the negatives and another not engaging with those negatives and focussing on the distorted picture that goes on.
For me I am happy to keep migration, but we need to think about how we share out those benefits from it. Currently the benefits are enjoyed overwhelmingly by wealthier people and I'd like to see firms who use migrant labour not have to list them, but have to ringfence money that could then be used to help support young people from all backgrounds with apprenticeships. Currently such a policy is not being developed because it goes against the internationalism of the left and the more knuckle dragging and laissez faire elements of the right who dominate the debate.