"To Listen" is very imported for a product manager. Listening is a skill, and for a product manager this skill is on the top of the skills list that a product professional must acquire. Effectiveness of core deliverable like identifying opportunities, writing business plan, collection requirements, PRDs, and release prioritization largely depends upon how well the product manager has mastered the skill of listening.
The purpose of listening for many as I observe is to reply. Start replying, even while the speaker continues to put his point or frame up reply while speaker is talking and start speaking as soon as he is done.
One of the major role a product manager (read expectations from product manager) is to consolidate inputs from various sources (read requirement gathering), compile them and take decision that would best benefit product & business strategy. It is hence imperative that product manager masters this skill of listening to its best.