why do the gods resemble human beings rather than other animals?

I am providing answer of your question from Aitareya Upanishad vreses.

Its said in the Upanishad that In the beginning the absolute Self was alone. Then He thought, "Let Me create the worlds." & He created the worlds.

स ईक्षतेमे नु लोका लोकपालान्नु सृजा इति सोSद्भ्य एव पुरुष समुद्धृत्यामुर्छयत् ||1.1.3||

Sa IkshaTeme Nu Loka LokaPaLaaNuu Sruja Iti
SoDbhya Eva Purusha SaMuDdhruTyaMurchhayat

He thought, "These then are the worlds. Let Me create the protectors of the worlds." Having gathered up a (lump of the) human form from the water itself, He gave shape to it.

So It’s said that the creator took lump (like clay) and given the shape to it like Purusha i.e a humanoid form Or figure - with head , hands etc. That we call as Virat purusha .

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Then he created the deities. And He subjected Him (i.e. Virat Purusha ) to hunger and thirst. Then the deities asked lord to provide the abode for them ,from where they can eat food. Then..

ताभ्यो गामानयत्ता अब्रुवन्न वै नोSयमलमिति |
ताभ्योSश्वमानयत्ता अब्रुवन्न वै नोSयमलमिति ||1.2.2||

Tabhyo GaaMaaNaYaTta AbruVaNna Vai NoYamLMiti
Tabhyo ShawaMaaNaYaTta AbruVaNna Vai NoYamLMiti

For them He (i.e. God) brought a cow. They said, "This one is not certainly adequate for us." For them He brought a horse. They said, "This one is not certainly adequate for us."

It’s said here that the lord bought the lump (Pinda) ,creature shaped like cow and horse. But the deities said that these shapes are not good for us to have our food in right way Or adequately .

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Then he bought the Virat Purusha in human form to them and they liked it.

ताभ्य: पुरुषमानयत्ता अब्रुवन् सुकृतं बतेति |
पुरुषो वाव सुकृतम् | ता अब्रवीद्यथायतनं प्रविशतेति ||3||

For them He brought a man. They said "This one is well formed; man indeed is a creation of God Himself". To them He said, "Enter into your respective abodes".

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Now although deities entered into their respective abodes i.e Indriyas ,but we can’t represent them like organs. Like we can’t graphically represent Prana Vayu as Or Mind as Chandrama. And even its not appropriate to represent deities like organs also cause then they will not look like divine beings.

Conclusion - So I think as deities liked this humanoid form because it is indeed the most beautiful creation of lord and found it appropriate to reside for receiving food I.e prayers etc. That indirectly means they specifically chosen this form in which they should have to be worshiped , We generally depict them in human form.And that is the reason why gods looks like human beings.

why do the gods resemble human beings rather than other animals?

I am providing answer of your question from Aitareya Upanishad vreses.

It's said in the Upanishad that In the beginning the absolute Self was alone. Then He thought, "Let Me create the world's". & then He created the world's.

स ईक्षतेमे नु लोका लोकपालान्नु सृजा इति सोSद्भ्य एव पुरुष समुद्धृत्यामुर्छयत् ||1.1.3||

Sa IkshaTeme Nu Loka LokaPaLaaNuu Sruja Iti
SoDbhya Eva Purusha SaMuDdhruTyaMurchhayat

He thought, "These then are the worlds. Let Me create the protectors of the worlds." Having gathered up a (lump of the) human form from the water itself, He gave shape to it.

So It’s said that the creator took lump (like clay) and given the shape to it like Purusha i.e a humanoid form Or figure - with head , hands etc. That we call as Virat purusha .

---

Then he created the deities. And He subjected Him (i.e. Virat Purusha ) to hunger and thirst. Then the deities asked lord to provide the abode for them ,from where they can eat food. Then..

ताभ्यो गामानयत्ता अब्रुवन्न वै नोSयमलमिति |
ताभ्योSश्वमानयत्ता अब्रुवन्न वै नोSयमलमिति ||1.2.2||

Tabhyo GaaMaaNaYaTta AbruVaNna Vai NoYamLMiti
Tabhyo ShawaMaaNaYaTta AbruVaNna Vai NoYamLMiti

For them He (i.e. God) brought a cow. They said, "This one is not certainly adequate for us." For them He brought a horse. They said, "This one is not certainly adequate for us."

It’s said here that the lord bought the lump (Pinda) ,creature shaped like cow and horse. But the deities said that these shapes are not good for us to have our food in right way Or adequately .

---

Then he bought the Virat Purusha in human form to them and they liked it.

ताभ्य: पुरुषमानयत्ता अब्रुवन् सुकृतं बतेति |
पुरुषो वाव सुकृतम् | ता अब्रवीद्यथायतनं प्रविशतेति ||3||

For them He brought a man. They said "This one is well formed; man indeed is a creation of God Himself". To them He said, "Enter into your respective abodes".

---

Now although deities entered into their respective abodes i.e Indriyas ,but we can’t represent them like organs. Like we can’t graphically represent Prana Vayu as Or Mind as Chandrama. And even its not appropriate to represent deities like organs also cause then they will not look like divine beings.

Conclusion - So I think as deities liked this humanoid form because it is indeed the most beautiful creation of lord and found it appropriate to reside for receiving food I.e prayers etc. That indirectly means they specifically chosen this form in which they should have to be worshiped , We generally depict them in human form.And that is the reason why gods looks like human beings.