JavaScript (177177 175 chars)
This is my best attempt at golfing this problem. I cannot find a way to do this with fewer characters
o='';
for(i=1;i<=26;i++) {
l='';
for(j=1;j<=i;j++) {
l+=String.fromCharCode(j+64);
}
o+=l+l.slice(0,l.indexOf(l.slice(-1))).split('').reverse().join('')+"\n";
}
console.log(o);