Lots of this is very sci-fi, but I figure without a hard-science tag, I can let fly with the theories. Funtastic!!! Here's my list that I could think up.
- Once they had regular tech, and that turned out badly, so they bioengineered everything.
- Extreme gene plasticity is present and any material can be produced.
- All the movie stars started using bio houses in the 1930s and it just took off!
- There was a "naturalist" social movement.
- Everything growing on this earth is already sentient, so the people took advantage of it.
- A memetic, living bio gel was found which took on characteristics of whatever it touched. This lead to many discoveries, but first, some horrors...
- Rolling EMP waves are present on this planet that would knock out anything run by electrics.
- Anything on this planet WITHOUT a bioorganic base quickly degenerates and disintegrates. For some reason the bonds between atoms don't work properly without LIFE installed, so there's a need for bio-based steel.
- Competition, BabyFree market competition! There were solid, non-bio based technologies, but an important discovery made bio-based cheaper, easier to produce AND better at handling certain jobs, and it just took over the whole market.
- Survival of the fittest. So someone invents bio-whatevers, and the bio-whatevers want more of themselves to be produced. The bio-whatevers actually send out spores or something like to either destroy anything that's merely matter or INFECT IT! Everything is bio-based because there isn't much that isn't infected with bio-smutz and for some reason, any matter material that humans work with starts to become bio-based. Humans figured out quickly that it was best that they guided the process rather than letting it run wild.
- Like @Zxyrra says--maybe some crazy dude in power decided this was the way. And it was.
- So, computers reached their zenith. We found we could not do more without incorporating bio-tech. And so, we did. And then we kept doing it.