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.
Note:
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.