If you want to reply to a Tweet with a Direct Message (DM) but you are unable to do so, here's a possible reason.
By default, you can only send DMs to the profiles that follow you on Twitter.
A workaround to this is you can Tweet your DM link in a reply to the user you want to send a direct message, or just ask them to follow you.
You can also take a look at these Direct Messages FAQ by Twitter to troubleshoot other queries.
There is an account limit of 1,000 Direct Messages sent per day. Once you reach this limit, you can’t send any more Direct Messages for the day.