There are some known issues on installing pyenv on macOS 11 (Big Sur).
Here is the solution that worked for me on macOS 11.2.2
$ brew install bzip2 lbzip2 lzlib openssl zlib
$ CFLAGS="-I$(brew --prefix openssl)/include -I$(brew --prefix bzip2)/include -I$(brew --prefix readline)/include -I$(xcrun --show-sdk-path)/usr/include" LDFLAGS="-L$(brew --prefix openssl)/lib -L$(brew --prefix readline)/lib -L$(brew --prefix zlib)/lib -L$(brew --prefix bzip2)/lib"
$ pyenv install --patch 3.8.0 < <(curl -sSL https://github.com/python/cpython/commit/8ea6353.patch\?full_index\=1)