Makes no sense to me. Does it to you? How can we possibly KNOW how many species have become extinct or how many there are currently?

No one can give you an exact number of living or even extinct species (the fact that we keep finding new and extinct ones proves that).  However they can give a general estimate.   The numbers they give are simply estimates based on what they do know.  Much like how they devise the number of stars in a galaxy or the number of galaxies in the universe.  Are these "guesses" accurate?  Perhaps... perhaps not.  No one can accurately say as no one knows everything. 

People have been going around cataloging any and every species they come across for thousands of years.  Even though the earth been here for quite some time, we still keep finding "new" species.  In fact, they've even come across several species that were once thought to be extinct (whoops!)   If one finds a fossil of a creature yet can no longer find a living example of that creature, then it's assumed to be extinct - and they keep finding those as well.  Of course some of those fossils aren't accurate either.  Several dinosaur species that they thought they had bones for were later found to be inaccurate (wrong bones put together).  

No exact numbers but yes, they can tell there were species that once existed and then died out.. In recent times we have more evidence of some of the species that have become extinct because they were recorded. Even so there may be many countless species we had not discovered, even recently, that have subsequently become extinct.

"Currently" is redundant. "How many there are" cannot be anything but current.

The fact that there is no answer to your question is mind boggling. No one can really know. It's like "How many stars are in the universe?" How could we answer that as we don't really know how big the universe is.

It's a scientific estimate. I am betting that religious folks are sceptical of that because God can't possibly made so many extinct before man even existed, can He?

There is no question we can never account for every species that has ever lived, nor can we count the current crop to an exact number. There are species which still escape our detection. 
But based on what has been catalogued, to include studies of the various historical mass extinctions, we can extrapolate at least a rough estimate of how many species have ever existed, and measure what we still know exists against that figure. The count of the former is still many, many times the count of the latter. 
Whether the true factor is 99% or something lower is purely academic, the point is still relevant, and I dare say, poignant. 

Sadly, the path to extinction has clearly accelerated since man has made his indelible mark upon the planet.