On An Argument for Irresistible Grace

I was having a discussion with a Calvinist friend of mine, and he presented this argument from analogy to me, and I thought it was interesting. He was wearing a hat, and he tossed the hat upon the table. He asks me, "Do you believe I just tossed the hat on the table?" I nod. "And did you have a choice in believing that I just tossed the hat on the table?" I say probably not. So likewise, when God presents us with His grace, we have no choice but to accept it. 

It's a cute and memorable argument. I don't think it really works though. So, I have this belief about his hat being tossed onto the table. Why? Because I visually sensed it and I abstracted from it with my intellect, and when my senses and intellect function properly, I have knowledge, and we are knowledge/truth oriented beings. So, it seems like a strange question to ask, where in the process of knowledge did I have a choice? 

It isn't clear that grace works in the same way. Grace is not originated in my senses, and I do not abstract anything from it. So while some knowledge may be involuntary, like when the form of a thing impresses upon my intellect involuntarily, grace is not something to be had by the intellect. We can know something about grace, but knowing something about grace and having grace are not the same thing. I may know something about your dog, but knowing something about your dog and possessing your dog are not the same thing. Grace seems to be something that affects the will more than the intellect, but it doesn't seem like the will can passively accept something like the intellect can (and I use passive in a non-technical way). So, the two cases aren't alike in the crucial way it needs to be, or at least, not obviously so.