Question

Why do all organic compounds contain carbon?

Answer 1

There's not much of a meaningful answer to this other than... It's been biologically successful for this to occur repeatedly. It works---asking this is like asking:

• Why does light contain photons? (because photons are defined as a quantum of light)
• Why do all proteins contain amino acids? (because amino acids are the basic building blocks of proteins)
• Why does earth have a self-sustaining environment? (because otherwise, why are we alive?)
• etc.

Well... because it's been sustaining life properly. It is what it is. Humans don't have to make organic compounds. Many are easily found in nature, and nature likes having carbon in organic compounds. :)

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As alternative phrasings to the above questions, it would be more practical in my opinion to ask:

• What about a photon is so special? (it's fast, it's indistinguishable from another photon, yet it has symmetric properties as a type of boson, allowing two photons to share the same quantum state, so there aren't moments where it's impossible for light to exist, etc.)
• What in a peptide bond is so good that all amino acids have them, being the basic building block of proteins? (they're rigid, they have great hydrogen-bonding capabilities, etc.)
• What kinds of natural processes are in line with earth's self-sustaining environment? (precipitation, evaporation, etc.)
• etc.