Theresa May statement after EU Brexit talks

The UK emphasizes the importance of mutual respect in negotiations with the EU, urging the EU to provide detailed counter proposals. The UK is preparing for a no-deal scenario, ensuring the rights of EU citizens in the UK and committing to prevent a hard border in Northern Ireland. The UK government stresses the significance of respecting the referendum result and seeks serious engagement to resolve negotiation issues.

Why does the speaker emphasize the legitimacy of the referendum result?

What are the two big problems mentioned in the negotiations that need to be resolved?