##05AB1E, 20 13 12 bytes##

A.p¦«vy¦«, 

Explanation

A.p  # push all prefixes of alphabet ¦« # concatenate each with it's reverse minus the first char   v  # for each string:   y¦« # concatenate with it's reverse minus the first char   , # print with newline 

Try it online

Saved 2 bytes thanks to Adnan.

05AB1E, 20 13 12 6 bytes

Saved 2 bytes thanks to Adnan.
Saved 6 bytes thanks to Magic Octopus Urn and some new language functionality.

Aη€ûû» 

Try it online!

Explanation

Aη # push prefixes of alphabet €û # palendromize each prefix û # palendromize the whole list » # join on newlines 

##05AB1E, 20 13 12 bytes##

A.p¦«vy¦«, 

Try it online

Saved 2 bytes thanks to Adnan.

##05AB1E, 20 13 12 bytes##

A.p¦«vy¦«, 

Explanation

A.p # push all prefixes of alphabet ¦« # concatenate each with it's reverse minus the first char v # for each string: y¦« # concatenate with it's reverse minus the first char , # print with newline 

Try it online

Saved 2 bytes thanks to Adnan.

##05AB1E, 20 13 bytes##

A.pvy¦«=}gF, 

Explanation

A.pv } # for each prefix of the alphabet y # bifurcate (push it and it's reverse) ¦« # remove first char of the reversed string and concatenate = # print while leaving on the stack g # length of top item (the longest string) F, # pop and print that many times (prints the lines of decreasing length) 

Try it online

Saved 3 bytes thanks to Adnan.

##05AB1E, 20 13 12 bytes##

A.p¦«vy¦«, 

Try it online

Saved 2 bytes thanks to Adnan.