Oh, Prue had arguments all right. She had a whole bag full of them. However, she knew he had several valid points - especially the fact that he could heal her, couldn't die and, of course, the family comment. Because while Prue prided herself on listening to her logic above her emotions, she also couldn't ignore the main part of an argument that she herself would have used were the situation reversed.
So instead she just fixed him with a patented I Am The Oldest And Therefore Know What Is Best look that she perfected courtesy of having Phoebe for a little sister. Then she stated simply, "Fine. You're coming with me. But if you're lying and actually can die, you better not do it on my watch. Otherwise, Chris is going to kill me."
With a shake of her head as well as a faint smile that stole across her features when she turned from him, Prue continued on her way. She knew, without bothering to check, that he would fall into step beside her. After all, what was the point of his little speech if he didn't make good on his intentions of joining her for this particular battle?