No. Sometimes the penis doesn't matter when breaking the hymen. By the time we reach puberty, our hymen has already begun to wear away. If it didn't, it would impossible for our menstrual blood to exit the body. A lot of women break their hymens through nonsexual means. This could include tampon insertion, horse or bicycle riding, dancing, gymnastics and other strenuous exercises. But yes, some women's hymens tear during the first time they have sexual penetration (that includes by penis, fingers, toys, etc.). If he has a thick penis and you have a somewhat-intact hymen, then your attempts to have sexual intercourse can result in some tearing. Tearing can also happen with a slimmer penis as well. Or, as I mentioned earlier, fingers and toys.
Some women have really thick hymens that are resistance to tearing. This an be a problem if they want to use a tampon or if they are having trouble having sexual intercourse. If this is the case for you, you can see your gynecologist, and s/he can gd a quick hymenotomy (this involves taking some surgical scissors and give the hymen a quick, surgical snip).
Here's more stuff you might want to know about the hymen: Magical Cups & Bloody Brides: Virginity in Context It's a really cool read, so do check it out!