Sourdough bread does have a slightly rubbery texture. Especially if you're not used to it, it might seem a bit odd at the beginning. It's also denser than your average yeast bread (and denser still than American bread, I think...) so it will be different to what you're used to.
If you find it too hard to get used to, you can find recipes that combine yeast with sourdough which makes the bread a bit fluffier