I think your friend is an idiot, sorry.
I have Factor V Leiden as well, as does my sister, my dad, his brother, and possibly my cousins (don't know them well enough to know the outcome).
It is not a given that it will be passed on, as my own brother doesn't have it - but since 5% of the British population do have this condition (that's 1 in 20 people) it's pretty common.
If you have homozygous (both genes carry the mutation) Factor V Leiden, it's more serious than if you have heterozygous (only one gene carries the mutation) - the risks are higher for clots - but aside from that, it doesn't really affect day to day life in most people.
We didn't even find out we had it until my uncle suddenly died from a PE in his 60s - Dad is his older brother and had got through life without incident until that point, but it was jolly useful to know for when he had an operation later and got a DVT. My sister and I were also glad to know for when we got pregnant, and could prophylactically use clexane to prevent clots. I also get a clexane jab before I fly home to the UK from Australia. It also means that we don't take the combined OC pill, and that HRT would be more of a risk than it's worth for us.
I am not making light of this condition but it's hardly a case for not having children! DS will be tested for it when he's old enough - at 4.8, there's no real need to test him (and it takes a fair bit of blood to do a full thrombophilia screen)
I have NEVER heard of anyone suggesting that a thrombophilic disorder should be a reason to not have children - especially given this one's prevalence in society - madness! Do you not think that some of the medics involved might have had a word? but they didn't! they just gave advice on how to a) achieve a safe pregnancy and b) avoid clots post partum.
Good grief.