I am using latest version macOS and homebrew, brew doctor find nothing wrong. and I just use brew install python,  brew install python@2 to get latest version of python.
When I type python -c "import sqlite3", I get following error messages:

python2.7 -c "import sqlite3"
  130 ↵ Traceback (most recent call last):   File "", line 1, in
     File
  "/usr/local/Cellar/python@2/2.7.15_2/Frameworks/Python.framework/Versions/2.7/lib/python2.7/sqlite3/init.py",
  line 24, in 
      from dbapi2 import *   File "/usr/local/Cellar/python@2/2.7.15_2/Frameworks/Python.framework/Versions/2.7/lib/python2.7/sqlite3/dbapi2.py",
  line 28, in 
      from _sqlite3 import * ImportError: dlopen(/usr/local/Cellar/python@2/2.7.15_2/Frameworks/Python.framework/Versions/2.7/lib/python2.7/lib-dynload/_sqlite3.so,
  2): Symbol not found: _sqlite3_enable_load_extension   Referenced
  from:
  /usr/local/Cellar/python@2/2.7.15_2/Frameworks/Python.framework/Versions/2.7/lib/python2.7/lib-dynload/_sqlite3.so
  Expected in: /usr/lib/libsqlite3.dylib  in
  /usr/local/Cellar/python@2/2.7.15_2/Frameworks/Python.framework/Versions/2.7/lib/python2.7/lib-dynload/_sqlite3.so
python -c "import sqlite3"
  1 ↵ Traceback (most recent call last):   File "", line 1, in
     File
  "/usr/local/Cellar/python/3.7.2_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/sqlite3/init.py",
  line 23, in 
      from sqlite3.dbapi2 import *   File "/usr/local/Cellar/python/3.7.2_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/sqlite3/dbapi2.py",
  line 27, in 
      from _sqlite3 import * ImportError: dlopen(/usr/local/Cellar/python/3.7.2_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/lib-dynload/_sqlite3.cpython-37m-darwin.so,
  2): Symbol not found: _sqlite3_enable_load_extension   Referenced
  from:
  /usr/local/Cellar/python/3.7.2_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/lib-dynload/_sqlite3.cpython-37m-darwin.so
  Expected in: /usr/lib/libsqlite3.dylib  in
  /usr/local/Cellar/python/3.7.2_1/Frameworks/Python.framework/Versions/3.7/lib/python3.7/lib-dynload/_sqlite3.cpython-37m-darwin.so

what may cause the problem? I tried to download python source code and compile it, and move the _sqlite3.so or _sqlite3.cpython-37m-darwin.so file into the brew installed folder, and everything works just fine. Could  brew just forget something in the formula? What can I do except for compiling .so file from source and manually solve the problem?
I finally find out where the bug hides.
All my macOS devices(including 2 Pros and 1 Air) are sharing the same .zshrc file, and for some reason, I add a
export DYLD_LIBRARY_PATH="/Users/myname/Library/Developer/Xcode/iOS DeviceSupport/10.0.1 (14A403)/Symbols/usr/lib/:/usr/lib/"
which ruins the build of python sqlite shared library file, for sqlite recently add a feature called '_sqlite3_enable_load_extension'.
when I removed the DYLD_LIBRARY_PATH to the outdated dir, and brew reinstall python everything is fine.
By the way, brew config and brew doctor provides no information about DYLD_LIBRARY_PATH. Next time I'll follow the rules and provide these informations.
Problem solved!
homebrew python@2 and python provides broken sqlite3