Here's a very short sample showing correct compilation against libxml2 on CentOS 6:

$ wget http://www.xmlsoft.org/examples/io2.c
--2017-05-31 15:13:18--  http://www.xmlsoft.org/examples/io2.c
Resolving www.xmlsoft.org... 91.121.203.120
Connecting to www.xmlsoft.org|91.121.203.120|:80... connected.
HTTP request sent, awaiting response... 200 OK
Length: 1182 (1.2K) [text/plain]
Saving to: `io2.c'

100%[======================================>] 1,182       --.-K/s   in
+ 0s      

2017-05-31 15:13:18 (53.9 MB/s) - `io2.c' saved [1182/1182]

$ gcc -o xmltest -I/usr/include/libxml2 -lxml2 -lz -lm io2.c
$ ./xmltest 
<?xml version="1.0"?>
<root>content</root>
$
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If you get the same then the problem is likely to be on the cpan side. But if you get something different then it isn't a perl problem at all and you'll need to fix your libxml2 installation.

I didn't compile libxml2. I got it from Red Hat rpms.

libxml2-2.7.6-21.el6_8.1.x86_64
libxml2-devel-2.7.6-21.el6_8.1.x86_64
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Just figured it out! I think this is a bug in the Makefile.PL. I added some print statements as suggested and ran it. It seems the makefile was only looking at the first '-I' and not all of them. I had '-I/usr/include/libxml2' as the third one. When I moved it to first, it ran successfully!

Thanks to everyone for their help! :)

It seems the makefile was only looking at the first '-I' and not all of them

Possibly an issue with your quoting (or lack thereof).
When giving multiple '-I' args to Makefile.PL's INC, you need to enclose them in double quotes:

perl Makefile.PL INC="-I/first/location -I/second/location"
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But if there's only one '-I' then you can do away with the double quotes.

Cheers,
Rob