Dissatisfied- bad customer care

I am flying on flight EK204 to Dubai. The flight was delayed in JFK by more than 1 hour. Emirates are now trying to change my connecting flight to another flight 20 hours later. The gate for my connecting flight EK770 only opens after the scheduled arrival so there is no reason I should incurr such a delay. None of the staff are willing to help to try and ensure that I make my connection. This is unacceptable as the delay was caused by their error originally. I am very dissatisfied.