Can species be paraphyletic?
You say that "only monophyletic groups are valid as species"... That is according to a certain interpretation of evolution that is not necessarily mainstream, (you wouldn't be taught that definition of species in Oxford or Yale) and which idealizes cladistics into simple trees, which don't reflect reality of hybridizing species like orchids and hominids, where simple tree like branching has been proven to not exist. Inflexible definitions of phylogeny should be taken with a pinch of salt, because pollen and other reproductive systems cause many species to be flexible. It's unwise to state that definition of species without being well aware of the mainstream one: Ernst Mayr definition. 

Strict interpretations of species lead to problems, because 
Darwin wrote:
No one definition of species has satisfied all naturalists; yet every naturalist knows vaguely what he means when he speaks of a species. Generally the term includes the unknown element of a distinct act of creation.

If you check the Wiki page on species, they state 11 contrasted definitions of species which are not necessarily cross compatible.   https://en.wikipedia.org/wiki/Species#Standard_definition:_Mayr.27s_Biological_Species_Concept

The definition of species that i was taught had nothing to do with the parental mechanisms that shaped the species differentiation from other species, and that it is a practical concensus to effectively group animals methodically, which doesnt actually reflect natures unmethodical reality. 

Seeing as humans interbred with neanderthal and denisovan species, and orchids interbreed very commonly, the following image refers to an idealized phylogenetic model which is not applicable to all reproductive systems, and it isn't applicable to humans.