We are a net importer of goods, we rely heavily on products from the eu. Which means the eu relies on selling to us, they don’t want to damage that with tariffs as it will cost their own businesses dearly.
The two statements don't necessarily follow. The UK relies heavily on the EU for about half of the food consumed, but the EU does not export half of its food production to the UK and so is not reliant on the UK market to anything like the same extent.
For most industrial and agricultural products, UK sales account for single figures - refuting the claim that 'they need us more than we need them'. VW sells approx. 10 million vehicles worldwide - only 250,000 of which are sold in the UK, so less than 3%. The figures are similar for the other car manufacturers, for EU food producers and for a whole range of products.
As for damaging EU businesses, although they will be impacted it is the British consumer that will be footing the bill. Taking cars as an example, every Ford, Citroen, Mercedes, BMW, Audi, Skoda, VW, Fiat and Dacia sold in the UK comes from the EU. Toyota, Kia, Hyundai, Mitsubishi and Jeep are also built in the EU for sale in the UK. All will cost 10% more after Brexit, as will the spare parts when they need repairing. The British consumer could buy a 'British' car, but these too will be more expensive as most of the parts come from the EU, and by 2022 there might not be a British car industry. Honda are already leaving. Nissan are getting nervous and can easily move to Renault in France or Dacia in Romania. JLR already have a new $1bn factory in Slovakia. BMW already make Minis in Austria and the Netherlands.
The same situation exists for exports. I'll let Theresa May explain:
In a stand-off between Britain and the EU, 44 per cent of our exports is more important to us than eight per cent of the EU’s exports is to them. The economic arguments are clear. Being part of a 500-million trading bloc is significant for us. One of the issues is that a lot of people will invest here in the UK because it is the UK in Europe.” ‘
“The reality is that we do not know on what terms we would win access to the single market. We do know that in a negotiation we would need to make concessions in order to access it, and those concessions could well be about accepting EU regulations, over which we would have no say, making financial contributions, just as we do now, accepting free movement rules, just as we do now, or quite possibly all three combined. It is not clear why other EU member states would give Britain a better deal than they themselves enjoy.”