Age difference between Barry Allen and Eobard Thwane

I can't speak to the motivation to the character in the show, but if they follow the motivation of the character from the comics.

Barry isn't alive in the future, the year Eobard Thawne is born, but has been immortalized by years of being a hero and the legacy he's left behind (it also helps that he builds a museum to himself)

Eobard Thawne (in the comics he goes by "Professor Zoom"), idolized Barry (to the point of being obsessive), and in an attempt to be more like Barry replicated the event that gave Barry his super speed. Eobard Thawne then used his new found powers to travel back in time to meet Barry face to face (in the comics he used the Cosmic Treadmill, not sure how they'll explain it in the show). However upon arriving in the past and finding out that he was destined to become a villain to Flash, Eobard Thawne became increasingly unstable, until he became the murderous psychopath we all know now as Reverse Flash.

Basically Eobard Thawne is the ultimate psychotic fanboy.

The nature of the show has resulted in fractured timelines where any of this could be correct and incorrect at the same time.

• Eobard Thawne was supposed to be born 2151.
• At some point in his younger life, he becomes the Arch-Enemy of an older Barry Allen, in Eobard's POV.
• In 2024, a younger Eobard and older (2024) Flash fight, disappear in an explosion, during a battle with Starling City's Green Arrow, The Atom, and Hawkgirl *.
• That fight is highly implied to lead Eobard and Adult Flash into 1999/2000, where Eobard attempts to kill 11 year old Barry.
• Older Flash Tells Present-day Flash to not save Nora. Older Barry saves 11 year old Barry. Reverse Flash Escapes.
• Eobard is stuck in 1999/2000. He stalks the Real Harrison Wells, kills him by taking his DNA to change his own shape.
• 14 Years later, Eobard-Wells causes the Particle Collider to be launched 6 years earlier than "History" says it was (Wells and Tess launched it in 2020 according to Eobard).

It's the second point that difficult to pin-point. As mentioned by other's, comic Eobard (Born in 2500s not 2100s) he has different power origins. First he recreates Barry's accident, gains powers, travels back in time only to find Barry's dead and starts to think he's Barry, until the third Flash, Wally West, defeats him, sending back to the future, forgetting the events. Then he finds Barry's suit in a time capsule, using it to gain the Flash's powers, only for Barry to have traveled into the future to see the time capsule open, where they fight. Defeated, Eobard travels back in time to fight Allen again and again.

So in the comics, Eobard and Allen fight over and over again due to constant time travel. If we extend this to the show, we can take Gideon's comment that Eobard has lost his ability to time travel to mean that it wasn't a one time thing. Eobard and Barry become enemies in the show due to multiple time travel events that have yet to be shown/explained. And with how malleable and inconsistent time travel and time is in the show, most of these events have both happened and not happened. It's a mess.

* _{The Justice League or similar exists in this timeline, and The Atom is alive. Current events show The Atom Ray Palmer is supposed to have died in 2015, at the end of Arrow Season 3, and the City was renamed to Star City, so this event may have or should no longer be in the real timeline}

Relax. I was having the same confusion. Then I read this:

"As I understand it, Reverse Flash traveled back and fought Flash in 2024. He then traveled back again to kill young Barry. Nothing unusual about Barry's age."

This isn't the fresh story where Zoom comes back in time and Flash and him become enemies. That's 2024. That's the whole story of Zoom. Coming from the future.

Don't confuse that story with the current TV story at hand.

The TV story is set when they comeback in time even more, around 2008 or something, and Zoom gets stuck and rest is all we see on TV.

Hope I don't need to explain why Flash stopped him younger self from stopping the murder of his mother.

Hint: Flashpoint Paradox.