No. If you are also on the lease agreement, then he cannot stand in the shoes of the landlord and require you to leave the property. You have as much legal right to be there as he does.
Practically speaking, however, if you are less than amicable, it might be best for you to part ways with your roommate.
DISCLAIMER: Brandy A. Peeples is licensed to practice law in the State of Maryland. This answer is being provided for informational purposes only and the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship. For legal advice relating to your specific situation, I strongly urge you to consult with an attorney in your area. NO COMMUNICATIONS WITH ME ARE TO BE CONSTRUED AS ARISING FROM AN ATTORNEY-CLIENT RELATIONSHIP AND NO ATTORNEY-CLIENT RELATIONSHIP WILL BE ESTABLISHED WITH ME UNLESS I HAVE EXPRESSLY AGREED TO UNDERTAKE YOUR REPRESENTATION, WHICH INCLUDES THE EXECUTION OF A WRITTEN AGREEMENT OF RETAINER.
Ms. Peeples is dead on correct, your roommate has no more right to remove you than you do to remove him. The only person that may remove you is the landlord and he/she must provide a proper notice under RCW 59.12.030 (non-payment of rent, illegal activity, breaking lease rules, end of lease or month to month termination).
This answer is for informational purposes only and should not be construed to establish an attorney client relationship. Before taking any legal action, it is always advisable to discuss your specific situation with an attorney.