Here was the problem: although there were hundreds of contacts on my iPhone, I only had an issue texting one contact. This person could text me without incident. However, if I replied or started a new text to them, it would always go out as a MMS email message. After checking and changing settings under the Messages heading on the iPhone, the same issue kept occuring.

Finally, I discovered the cause of the problem with this one client. They were in my contacts twice – one entry had their email address and their phone numbers, including their mobile number which I was trying to text. The second entry had a slight variation of their name and only the email address – the same email address as the first entry. When I deleted the contact that only had the email address, my texts to this person went out as texts and not emails. The issue was resolved.