On macOS Sierra 10.12, I ran into issues updating my gems that relied on Nokogiri due to the following error with the OS libxml2 version.

Building native extensions.  This could take a while...
ERROR:  Error installing nokogiri:
        ERROR: Failed to build gem native extension.
 
    current directory: ~/.rbenv/versions/2.3.1/lib/ruby/gems/2.3.0/gems/nokogiri-1.6.8.1/ext/nokogiri
~/.rbenv/versions/2.3.1/bin/ruby -r ./siteconf20161013-4537-ttdfzl.rb extconf.rb
checking if the C compiler accepts ... yes
checking if the C compiler accepts -Wno-error=unused-command-line-argument-hard-error-in-future... no
Building nokogiri using packaged libraries.
Using mini_portile version 2.1.0
checking for iconv.h... yes
checking for gzdopen() in -lz... yes
checking for iconv... yes
************************************************************************
IMPORTANT NOTICE:
 
Building Nokogiri with a packaged version of libxml2-2.9.4.
 
Team Nokogiri will keep on doing their best to provide security
updates in a timely manner, but if this is a concern for you and want
to use the system library instead; abort this installation process and
reinstall nokogiri as follows:
 
    gem install nokogiri -- --use-system-libraries
        [--with-xml2-config=/path/to/xml2-config]
        [--with-xslt-config=/path/to/xslt-config]
 
If you are using Bundler, tell it to use the option:
 
    bundle config build.nokogiri --use-system-libraries
    bundle install
 
Note, however, that nokogiri is not fully compatible with arbitrary
versions of libxml2 provided by OS/package vendors.
************************************************************************
Extracting libxml2-2.9.4.tar.gz into tmp/x86_64-apple-darwin15.5.0/ports/libxml2/2.9.4... OK
Running 'configure' for libxml2 2.9.4... OK
Running 'compile' for libxml2 2.9.4... ERROR, review '~/.rbenv/versions/2.3.1/lib/ruby/gems/2.3.0/gems/nokogiri-1.6.8.1/ext/nokogiri/tmp/x86_64-apple-darwin15.5.0/ports/libxml2/2.9.4/compile.log' to see what happened. Last lines are:
========================================================================
    unsigned short* in = (unsigned short*) inb;
                         ^~~~~~~~~~~~~~~~~~~~~
encoding.c:815:27: warning: cast from 'unsigned char *' to 'unsigned short *' increases required alignment from 1 to 2 [-Wcast-align]
    unsigned short* out = (unsigned short*) outb;
                          ^~~~~~~~~~~~~~~~~~~~~~
4 warnings generated.
  CC       error.lo
  CC       parserInternals.lo
  CC       parser.lo
  CC       tree.lo
  CC       hash.lo
  CC       list.lo
  CC       xmlIO.lo
xmlIO.c:1450:52: error: use of undeclared identifier 'LZMA_OK'
    ret =  (__libxml2_xzclose((xzFile) context) == LZMA_OK ) ? 0 : -1;
                                                   ^
1 error generated.
make[2]: *** [xmlIO.lo] Error 1
make[1]: *** [all-recursive] Error 1
make: *** [all] Error 2

Installing libxml2

I’ve found installing libxml2 from homebrew to work in the past:

brew install libxml2

Finally, you’ll need to do one of two things depending on how you are performing the update:

Bundler

With Bundler, you need to instruct it to configure Nokogiri builds to use our newly installed libxml2 library:

bundle config build.nokogiri --use-system-libraries --with-xml2-include=/usr/local/opt/libxml2/include/libxml2

On the next run of bundle update, it should install correctly

Rubygems

A gem install allows you to pass in the configuration options to the native extension using --:

gem install nokogiri -- \
  --use-system-libraries \
  --with-xml2-include=/usr/local/opt/libxml2/include/libxml2