Say, a typical lifetime of humans are 65 years old.
And there are 365 and a quarter days in a solar year
And there are 24 hours in a day
And 60 minutes to an hour
And typically, a healthy adult breathes 18 times in a minute (Source: Wikipedia) I picked 18 out of typical randomness.

65 * 365.25 * 24 * 60 * 60 * 18 = 36,922,392,000.

So with your theory, breathing has a 1 in 36 billion chance of dying.

The sperm can't "swim up" and "meet" the egg. And considering the location of the egg is quite hard to reach, it usually takes quite a sizeable amount of semen and vaginal liquid to facilitate the environment required to reach there.

While it does take a mere sperm to fertilize an egg, a drop of semen outside your vagina isn't sufficient for this. The ovum is located way back inside the fallopian tube.

If you're not in the ovulation period, the cervix would be plugged anyway.

But then, as with most sex-education articles, they're biased towards prevention rather than true, verifiable scientific possibility. Prevention is better than cure as accidental pregnancy is quite a disaster.

By the way, what is preventing the nurse to call you just by name like most other clinics do?