draw in this sentence means to pull toward. like how a sponge will draw the water up into its pockets to be absorbed. example I was drawn into her beautiful eye/ I was pulled into her beautiful eyes, and the meeting has not happened yet so they will meet. meet is the action and should be thought of as to meet, so its possible to meet or have a meeting. just like we can eat or we could have eaten but we cant have eat...so we can meet or have a meeting but no have meet