[allmendream]

Because the tissue wasn't “soft” until it was demineralized.

And the minerals in bone are not the same as the minerals in a fossil.

The dinosaur bones were fossilized, they were not just bone that had been softened.

So why is it that we find actual bones of modern species, but only fossilized bones of dinosaurs? Why are there not human and horse skeletons found that are fossilized to an equal degree?

[GodGunsGuts]

That’s why forensic scientists demineralize bones all the time to get at the soft-tissue contained therein. LOL

[count-your-change]

“soft tissue” simply means everything but bone its self and softening bone by acid treatment doesn't turn it into “soft tissue”. A chicken wing off my table might be acid treated to free up the collagen and other soft tissue for examination.
Straining at gnats will get you lots of gnats but not much else.

There are two ways for things to become fossilized, either replacement of the original substance with new mineral or covering over the object and thus preserving it.
It appears the tissue in the article was of the second kind.

Modern species? How modern? Mammoths, Middle Ages, Monday last?

“Why are there not human and horse skeletons found that are fossilized to an equal degree?”

You haven't offered any info. to suggest what it is you're asking. Why would we expect them to be fossilized to an equal degree? Or not?