Your problem is twofold:
- The person who likely replaced the starter in the past either had "ham fists" and muscles enough to run them badly (and/or a bottle or Loctite), or;
- The toolkit you received as a Christmas gift is made out of the cheapest steel in the world (as are most ALL "consumer-quality" tools these days)
There is about a zero percent chance that the bolt was replaced with a left-handed thread one, but there IS a chance you forgot one of the basic tenets of mechanix - mainly, "Righty-TIGHTY, Lefty-LOOSEY".
I think it is more likely you simply need the proper tools for the job, mainly a HIGH QUALITY (read "Profession Grade Lifetime Guarantee") 3/4" drive, the right-sized 6-POINT SOCKET, matched to a properly sized 3/4" extension bar (long enough to give you the whatever clearances you need to really lay the meat to twisting the bolt), and either a HIGH QUALITY solid 3/4" "Breaker Bar" or HIGH QUALITY 3/4" ratchet handle, either with at least a 16 inches or so of length, so you can truly "reef" on that puppy.
I do NOT mean any of the "Lifetime Guarantee" tools you can get at a big box store, I mean a true "Professional Quality" tools like Proto or Snap-On. Other makes like Craftsman and that ilk used to be good, but many years ago the manufacturers figured out they could make a LOT more money with really cheap tool steel and casting the words "Lifetime Guarantee" into the tools. I am sure you probably will not go too far out of your way to replace those tools that have already "melted" in your hands trying to do this "simple" job - and they count on that.
The proper 3/4 inch drive tools for that job - the socket, the extension and the long-handled ratchet or breaker-bar will likely cost more (x2) of what the new starter will cost. You will need to beg, borrow or steal them. I would not recommend attempting to steal them, as most mechanics who possess tools of that quality depend on them for their livelihood and safety, which is to say they love and trust them even more than their own spouse.
After you garner the right tools, you must figure out how to use them PROPERLY! Used improperly, you can turn trying to twist that one, single bolt off into an $800-plus major repair job in about 2 1/2 seconds, or even worse, you can easily EASILY knock every tooth out of the front of your face INSTANTLY, before you understand what hit you.
(Never EVER pull tools of that size and mass towards you, you always push them away from you while using!!!)
Pushing the handle away from you, you will also need to apply exactly the same amount of pressure in the opposite direction to the top of the handle or ratchet, all while pushing the whole assemble in towards the bolt, it at an additional equal or greater force.
In other words, you need to not simply turn the bolt off, you must work the forces in three separate directions, and all of them AWAY from you. That usually means you will be handling big, heavy tools in exactly the OPPOSITE direction as you did last time, using both hands to apply forces in x3 directions - and it will still be a "bear" to remove.
If you really choose to get the right tools and do this yourself, don't forget the additional items you will need:
1) Beer, all "Shade Tree Mechanics" work better with a few beers in them (it numbs the pain when the wrench slips),
2) BANDAGES and a Cell Phone; those little wrenches you initially used might cause a skinned knuckle or two, but the "Big Boys" will cause broken bones and major lacerations - the bandages help while waiting for the ambulance you might need the cell phone to call,
3) A helper - someone to hold your beer after you utter those famous last lines "Hold my beer, and watch this!", and who will call your mom later to tell you what hospital they took you to.
4) and last but not least, a brand-new, properly sized and length replacement bolt for the over-torqued one you are removing, and a properly pitched tap to chase the bunged up threads with.
There is a reason a good mechanic costs a few bucks: outside of the training, experience and $50,000.00 - plus worth the tools in that tool-box of his, he usually works in a pretty nice shop, not on his back under a truck in the Target parking lot, where some little old man in a three ton Cadillac, wearing a silly plaid hat and those goofy big "I've just been to the Optometrist and had my eyes dilated" sunglasses can run over his legs.
Good luck, Chad!
