The phrase "throw something open" can mean to make something available to the public or to open something up for discussion. There are several synonyms for this phrase, including "unveil," "expose," and "reveal." Alternatively, you could use "make accessible," "open up to," or "make available." If you want to emphasize the idea of discussion, you might choose "put up for debate," "invite input," or "bring to the table." No matter which synonym you choose, it's important to convey the idea that something is being made accessible or available, and that people are invited to participate in some way.