PowerShell v2+, 175 169 163 154 bytes
($x=(-join(65..67+66..86|%{$_;32+$_}|%{[char]$_})-split'(.{6})'-ne'')+' WwXx'+' Yy'+(' '*9+'Z')|% *ht 10|%{$_+-join$_[9..0]})
' '*9+'zz'
$x[10..0]
Try it online!
Abuses the fact that default Write-Output at the end of execution inserts a newline between elements.
The first line constructs the branches. We loop over two ranges corresponding to the ASCII values for the capital letters, each iteration output a char array of that letter and that letter +32 (which is the lowercase ASCII point). That's -joined together into one long string, then -split on every six elements (encapsulated in parens so they're preserved), followed by a -ne'' to pull out the empty elements as a result of the split, thus forming an array of strings.
These strings in an array get array-concatenation to add on the WwXx, Yy, and Z elements, then a PadRight 10 to make them all the appropriate width. At this point we have an array of strings like the following (one element per line).
AaBbCc
BbCcDd
EeFfGg
HhIiJj
KkLlMm
NnOoPp
QqRrSs
TtUuVv
WwXx
Yy
Z
That whole array is piped to another loop to construct the mirrored strings with -join and array-reversing [9..0].
AaBbCc cCbBaA
BbCcDd dDcCbB
EeFfGg gGfFeE
HhIiJj jJiIhH
KkLlMm mMlLkK
NnOoPp pPoOnN
QqRrSs sSrRqQ
TtUuVv vVuUtT
WwXx xXwW
Yy yY
ZZ
We save the resulting strings into $x and enclose in parens to also place a copy on the pipeline.
The next line places the zz string on the pipeline, then the $x array in reverse order. All of those are left on the pipeline and output is implicit.
PS C:\Tools\Scripts\golfing> .\alphabet-chromosome.ps1
AaBbCc cCbBaA
BbCcDd dDcCbB
EeFfGg gGfFeE
HhIiJj jJiIhH
KkLlMm mMlLkK
NnOoPp pPoOnN
QqRrSs sSrRqQ
TtUuVv vVuUtT
WwXx xXwW
Yy yY
ZZ
zz
ZZ
Yy yY
WwXx xXwW
TtUuVv vVuUtT
QqRrSs sSrRqQ
NnOoPp pPoOnN
KkLlMm mMlLkK
HhIiJj jJiIhH
EeFfGg gGfFeE
BbCcDd dDcCbB
AaBbCc cCbBaA
-9 bytes thanks to mazzy.
14It doesn't make much sense that the first two lines both contain B and C when all other lines (bar the mid section) have unique letters. – Fatalize – 2016-08-23T14:38:06.807
1@Fatalize That's to make the challenge slightly more interesting – Beta Decay – 2016-08-23T15:44:18.067
5I would personally argue it does the opposite – Fatalize – 2016-08-23T17:26:34.930
2I believe there's a mistake in the 9th line. Should be "WwXx xXwW", not "WwXx xXWw", shouldn't it? – GOTO 0 – 2016-08-23T18:58:57.863
You probably should've used the Sandbox to get feedback before posting. – Mego – 2016-08-23T22:10:03.887
2@BetaDecay Fatalize is right, that makes the challenge more boring. – moonheart08 – 2019-03-07T15:56:04.867
Are trailing spaces allowed per line or only at the text block's end? – Jonathan Frech – 2019-09-22T00:40:43.023