Emails not recieved not their responsibility

We have been a Afrihost client for 2 years, we recently switched to a managed dedicated server. Since the switch we have not been receiving emails from certain email address, even though they receive ours. After several hours on the phone and emails back and forth we were basically told they checked the server and it is not theirs problem but the person who is sending us the emails. I can't understand how this is the case as it is from more than one company, and we received emails from them with no problem until we switched over to the dedicated server. We are also unable to send or receive any mails to or from any Hotmail account which basically means there are thousands of people who have to check their side? We tried to move away from Afrihost and a cancellation was done on the 25th of Feb 2015 and by the 6th of march they had not released our domain or pointed the MX to the right IP so we were forced to return to Afrihost, which has just been endless problems. The average hold time is at least 7mins just to speak to someone. It is a complete mystery to me how Afrihost has been voted top ISP for numerous years when this is the customer service received.