It might be clearer if you read it as "detect THE single particle passing through the slits"
If you use a strong light then there are lots of photons passing through the slits and the interference could be completely classical with different photons going through each slit and interfering at the screen - just like water waves. This was the picture for 100s of years.
With modern detectors it is possible to use a very faint light source so that there is only a single photon in flight at a time - and yet still see interference. So the particle is interfering with itself!
If you are trying to detect which slit the particle goes through and show that knowing this destroys the pattern then you need to have only one particle at a time. Otherwise you could detect which slit a single photon goes through but the billions of other photons would still make a normal patter