This paper presents a novel teachable conversation interaction system that is capable of learning users preferences from cold start by gradually adapting to personal preferences. In particular, the TAI system is able to automatically identify and label user preference in live interactions, manage dialogue flows for interactive teaching sessions, and reuse learned preference for preference elicitation. We develop the TAI system by leveraging BERT encoder models to encode both dialogue and relevant context information, and build action prediction (AP), argument filling (AF) and named entity recognition (NER) models to understand the teaching session. We adopt a seeker-provider interaction loop mechanism to generate diverse dialogues from cold-start. TAI is capable of learning user preference, which achieves 0.9122 turn level accuracy on out-of-sample dataset, and has been successfully adopted in production.