Why is Rudra called Pashupati?

Pashu means those whose which are tied and thus Pashupati literally means Lord of those which are tied. Pashu also means Cattles/Animals, and Pashupati also means Lord of Animals.

The name PashuPati is given 3 times itself in the Veda Samhita in the Sri Rudram. 

The 2nd Anuvaka states "Pashunam Pataye Namaha", 8th Anuvaka states "Nama Sangaye Cha Pasupataye Cha" and particularly 5th Anuvaka states:

नमो भवाय च रुद्राय च। नमश्शर्वाय च पशुपतये च।

Salutations to him who is Bhava, who is Rudra, who is Sharva and who is PashuPati.

Yajurveda states:

येषामीशे पशुपतिः पशूनां चतुष्पदामुत च द्विपदम् ।। [YajurVeda 3.1.4]

Which Pashus do the Pashupati rules? He rules both the two footed and four footed.

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A forerunner for this concept is available in Rig Veda I.114.1 & 9, dedicated to Rudra, in a subtle manner.

इ॒मा रु॒द्राय॑ त॒वसे॑ कप॒र्दिने॑ क्ष॒यद्वी॑राय॒ प्र भ॑रामहे म॒तीः । यथा॒ शमस॑द् द्वि॒पदे॒ चतु॑ष्पदे॒ विश्वं॑ पु॒ष्टं ग्रामे॑ अ॒स्मिन्न॑नातु॒रम् ॥१॥

These poetic thoughts do we proffer to Rudra, the powerful one with braided hair who rules over heroes, so that he will be luck for our two-footed and four-footed, so that everything in this settlement will be flourishing, free of affliction.

In the mantra 9 of the same Hymn, the poet describes himself as cowherd - पशु॒पा, indicating that the owner is Rudra, an epithet of the Almighty.

उप॑ ते॒ स्तोमा॑न् पशु॒पा इ॒वाक॑रं॒ रास्वा॑ पितर्मरुतां सु॒म्नम॒स्मे । भ॒द्रा हि ते॑ सुम॒तिर्मृ॑ळ॒यत्त॒माथा॑ व॒यमव॒ इत्ते॑ वृणीमहे ॥९॥

Like a cowherd, I have driven these praises close to you. Grant your favor to us, father of the Maruts, for your benevolence is auspicious, most merciful. It is just your aid that we choose.