What you wrote above is why he doesn't want to do therapy via email and why he kept suggesting you contact him for a session. Such written communication is not productive and easily misinterpreted.

You wanted an email reply. He apologised for the delay and sent you a reply. Now, you read the tone of the email as 'cold'. I am not blaming you - just that written communication *is* subject to misinterpretation as we don't hear the tone or see the person.

if you want support, speak to him. Email can only make things worse (he didn't reply or he didn't say what you expected him to or he did not address what you wanted etc. etc. etc.)