pip doesn't check that the package has been updated for your Python version. It seems that pysqlite hasn't - from the log file:
File "/tmp/pip_build_root/pysqlite/setup.py", line 85
print "Is sphinx installed? If not, try 'sudo easy_install sphinx'."
^
SyntaxError: invalid syntax
This is a SyntaxError because print is a function in Python 3, not a statement. The only solution to this is to use a package that has been updated, or to update this one yourself. You might consider whether the builtin sqlite3 module meets your needs. As far as I can tell, it seems to be the same module; it is certainly, according to the docs, originally written by the same person.