Using 'drag in' can suggest the speaker is irritated about the topic being introduced. He always drags in his personal problems, even in professional meetings.
Pro Tip 2/3
Unwanted Topics
'Drag in' often implies the topic is unwanted or disrupts the flow of conversation. Let's not drag in our disagreements into the party tonight.
Pro Tip 3/3
Subtle Warning
Can be a polite way to indicate someone is going off-topic without direct confrontation. I wish you hadn't dragged in that old argument into our discussion.