Was Hanuman the son of Shiva?

Since childhood we all have been hearing that Hanuman is an incarnation of Shiva. But in this blog, I'll show you a twist in the tale proving that Hanuman is the son of Shiva.

The first proof is that in the Hanuman Chalisa, Hanuman is known as Shankar Suvan. In the Shiv Chalisa, Ganesha is known as Girija Suvan. Girija here is Parvati and Ganesha is the son of Parvati. This means that Suvan means son. This also means that Hanuman is the son of Shankar, a name of Shiva. 

Now have you ever wondered why Tulasi leaves are offered to Hanuman but not to Shiva? Tulasi cursed Shiva that her leaves would never be given as an offering to Shiva as he had killed her husband named Jalandhar. If Hanuman was an incarnation of Shiva, then why would have Tulasi leaves been offered to Hanuman? Why are Bilva leaves, which are dear to Shiva, not offered to Hanuman?

Also to state that giving vermillion to Hanuman is auspicious but giving vermillion to Shiva is inauspicious. Had Hanuman been an incarnation of Shiva, then offering vermillion to Shiva would not have been inauspicious.

One legend says that Hanuman was born through the falling of the semen of Shiva which was transported to Anjana's womb with the help of Vayu. In the same way Kartikeyan was born by the falling of the semen of Shiva which had fallen into the river of Ganga, carried by Agni, fell on Bhudevi and sent to Krittikas. Even the semen of Shiva fell which was later transported to the womb of Kadru, the wife of Kashyap, as a result of which Mansa was born. If Hanuman is the incarnation of Shiva, then why is Kartikeyan not considered to be the incarnation of Shiva? This shows that Shiva and Vayu are the spiritual fathers of Hanuman while Anjana and Kesari are the biological parents of Hanuman.