Why is Zen/Chan thought to be more related to Buddhism than to Taoism? According to the book The Tao of Zen, Zen/Chan is esentially a form of Taoism. This makes sense to me, as it's hard to understand what is the common ground between the relative simplicity of Zen and the baroque belief systems of the other Mahayana traditions.

However, this is not a predominant opinion about the origins of Zen. I understand that it is generally believed that Zen is a branch of Buddhism, with some Taoist influences. What are the arguments that support this opinion? Has anybody provided counter-arguments to the ones presented in The Tao of Zen?
the relative simplicity of Zen and the baroque belief systems of the
  other Mahayana traditions


Are we talking about style? Yes, the records of the Zen masters resemble the style of the Zhuangzi more than they resemble the style of the Avatamsaka Sutra. But we should be more interested in content when evaluating where a tradition belongs. - The Sutras are written in a highly intricate, metaphorical language. Like the Zen master Bassui said: "Before we can read the Sutras, we have to open the mind that can read them." The Sutras are addressing a reality that is sometimes not available to an unenlightened mind.


  it is generally believed that Zen is a branch of Buddhism, with some Taoist influences. What are the arguments that support this opinion? Has anybody provided counter-arguments to the ones presented in The Tao of Zen?


Every scholarly book written on the origin of Zen is a counter-argument. 

Let's look at a few salient points - off the top of my head:

1) The Zen school was not called that at first. It was known as the "Buddha-Mind School" and the Zen masters were referred to as "the Lankavatara Masters":


  In its beginnings in China, Zen primarily referred to the Mahāyāna
  sūtras and especially to the Laṅkāvatāra Sūtra. As a result, early
  masters of the Zen tradition were referred to as "Laṅkāvatāra
  masters". In other early texts, the school that would later become known as Zen is sometimes even referred to as simply the "Laṅkāvatāra school" (Ch. 楞伽宗, Léngqié Zōng). Accounts recording the history of this early period are to
  be found in Records of the Laṅkāvatāra Masters (Ch. 楞伽師資記, Léngqié
  Shīzī Jì).


(cf. Dumoulin, Heinrich (2005-A), Zen Buddhism: A History. Volume 1: India and China, World Wisdom Books, ISBN 978-0-941532-89-1 )

The whole school was called after a specific sutra, named the  Laṅkāvatāra. 

The First Patriarch of Zen is said to have handed this sutra to the Second Patriarch as containing the essentials of the school teachings. 

If you study that Sutra closely, you will realize that it has all the essential teachings of Zen, and since it predates Zen, it is only reasonable to conclude it is the source. The main idea there is that "mind is buddha", that it all comes down to the mind of the sentient being; that everything is a projection of the One Mind (which is also what Huangbo says verbatim).

2) The Sixth Patriarch in the Platform Scripture says quite explicitly that to practice Zen, one has to study and recite the Diamond Sutra. Why does he single out that sutra and not the Zhuangzi or the Daodejing?

3) All the Zen masters used Mahayana Buddhist language and terminology: samsara, nirvana, bodhisattva, tathagata, etc. compare with how often they use terms such as qi, yin/yang, Heaven (in the Taoist sense), etc. It's not even up for debate. They overwhelmingly use Buddhist language.

4) They were all Buddhist monks, with Buddhist robes, shaved heads, etc. I mean, this is an obvious fact. Why stay in a Buddhist monastery if you're a Taoist?

5) All they say is traceable back to Mahayana Philosophy. Everything. The One Mind, transcending samsara, non-duality between samsara and nirvana, mind being buddha, truth being beyond language, silence as a teaching etc. Even the dismissal of Sutras is ultimately traceable back to the Sutras!

There's nothing original in the ideas of the Chan school:


  There is nothing unique about Ch'an doctrine; it is an eclectic form
  of Mahayana philosophy. So there is no contradiction involved in a
  tradition of meditation practice co-existing with the sectarian
  doctrines of the various sects of Chinese Buddhism. Masters whose
  names appear in the succession-lists of both Ch'an and another
  sectarian tradition would simply be both dharma- and dhyana-masters in
  their respective monasteries.


Charles W. Swain, The Emergence Of Ch'an Buddhism, Chung- Hwa Buddhist Journal vol.2/Oct, 1988 P.391-399



In fact, if there's anything original, it's the style. If there's anything that cannot be traced back to Indian Mahayana - is exactly the style, the form their upaya takes, and not their doctrines, not their insights. 

But why call that style "Taoist" and not instead call it "Chinese"? Perhaps there's some common source both Chan and Taoism are drawing from, and that has more to do with the Chinese character, that manifests there as abrupt and direct? What makes more sense instead is that Buddhism is adaptable, and so it takes many forms depending on the country and the spirit of the country where it takes root.