So this means that the lack of isolation is inherent in the headphones themselves.
The amount of isolation is a property of the headphone. For example, a good Active Noise Cancelling (ANC) headphone will typically also have good "passive noise cancellation", a.k.a. isolation, whereas a good open planar magnetic headphone will often be as loud on each side of the cup, as if it was just a speaker held in space.
my friend told me that he could still hear the music leaking.
Did your friend put their ear against the cup and correctly claim that they could hear something, or were they in the next room shouting at you to turn down the noise?
I hope I did not get faulty headphones. Is everyone facing the same situation as I do?
Let's work on the assumption that you did not while we solicit everyone's feedback (which may take a while).
I actually could still return them if this is the right thing to do. What do you think?
I think we need to get some more precise and detailed answers to questions about you, your requirements and your environment.
I am only wearing the headphones at home but I just don't like the fact that they are leaking sound
Since enjoying music is a purely subjective experience, what we like is what matters. That said, things which are incidental to the listening experience really shouldn't be a consideration when assessing equipment. Rather than ask why you care about this, perhaps you could explain it in terms of a problem, i.e. how are you identifying and/or measuring an adverse consequence?
I suspect that this may be due to the wood they use on the cups, it seems that wood doesn't efficiently isolate sound.
Another case of degree being confused with an absolute. Wood is just a material, like concrete or paper, which can vary in properties relevant to sound absorption, reflection and scattering depending on multiple factors including the type of wood, its treatment, density, finish, shape, position relative to the driver, coupling, etc. As a category of material for headphone cups, it is generally
a good choice. See e.g. the audiovisual pornography which is
ZMF, especially the kaleidoscopic
Vérité Closed Stabilized.