its really simple; hes throwing it out because you will come back in the room to give it to him.
what hes saying that he wants is your attention and companionship.
is he taking 2 naps a day? perhaps he needs to downsize to only 1 nap. is he taking just one nap a day? maybe he needs 2 small naps instead. watch him closly in the next few days to see if and when he is showing signs of being tired. rubbing eyes is a big one.
but you might have to make some family life adjustments. especially at night. he wants to be near you, you to be near him. i see nothing here that would be solved by putting him in a big kid bed. he will just get up and try to come find you instead.
perhaps you have to change your routines. maybe he needs your direct complete attention before nap and bedtimes in order to calm down. its funny because my 3 year old is doing this right now. he is in his crib that converts to a toddler bed... so hes in the toddler bed phase. so he can get up, and trust me, he does. what he wants is for me to calm him down. i know that because he tells me.
ask your son if he needs you to calm him down a bit. sometimes when kids are playing or whatever, they are too stimulated to be able to relax, especially if they are overtired or not tired yet. (you know your child and you should know that he DOES need to sleep at this age).
anyway, ask him. see if he will tell you. do things for him : rocking him, rubbing his back, reading him a gentle story (nothing exciting or anything), sing songs to him, or just hold him and relax your breathing and take a rest yourself. tell him you are helping him calm down (this will give him the words to use later!) and see if that helps.
otherwise, you could go the more difficult option and just stop giving him the blanket. its all up to you and your parenting choices. but i recommend the more emotionally sensitive decision. you know your son right? just trust that he is trying to tell you something and try your best to figure out what it is. listen to your heart.
he could also be teething.... check his gums for any teeth poking through - redness, swelling, or white colored gums.... give him tylenol to see if hes just got some pain.