The following article contains spoilers from Batman #126, on sale now.
Batman's new enemy, Failsafe, finally had his first encounter with the Dark Knight. Batman #126 (by Chip Zdarsky, Jorge Jimenez, Tomeu Morey, and Clayton Cowles) saw the two go head-to-head. Or rather, it saw Failsafe wipe the floor with Batman, catching him off guard in his own cave, chasing him down, and terrifying him with how much faster, stronger, and stealthier he is.
In other words, Bruce got to experience what it is like when he terrorizes ordinary criminals. Failsafe put the fear of Batman into Batman. It was a humbling experience, but one that might have been more than an attack. Failsafe is clearly trying to take Batman's place, so this attack may have been an audition to prove that he is a worthy replacement.
Despite being a large robot, Failsafe seems to have all of Batman's best qualities programmed into him. The first implication of this is how easily he infiltrates Batman's mini-cave, sneaking up on him without anyone being the wiser. Even Batman didn't pick up on it until it was almost too late. From there, the fight was heavily in Failsafe's favor. His superior strength made it easy for him to toss Batman around like a rag doll.
What truly stuns Batman, though, are Failsafe's other abilities. He is far faster than his mechanical form would indicate, giving Batman few opportunities to formulate a plan of attack or even escape. Then there is his stealth. To sneak up on Batman the way Failsafe did is no small feat. It terrified him that something so big could be so quick and so silent. It made him feel as though he was up against a force of nature rather than a physical thing. That, though, is exactly how the average criminal feels when Batman goes after them.
To be put up against a high-ranking foe who seems to defy what should be possible is a terrifying experience. Batman rarely gets intimidated in such a manner. It's almost as if Failsafe is trying to flex his skills for Batman. To show him that he is a better vigilante while also removing the competition.
This isn't too far outside the realm of possibility. Failsafe obviously has some type of connection to Batman, most likely being set up as his successor in the event he becomes unable to protect Gotham. The robot also has a personality and is capable of making his own decisions. Proving his supremacy to Batman might have been both a courtesy and a scare tactic.
By dominating Batman in fields that he is usually unchallenged in, Failsafe shows that he is more than capable of doing what Batman does. However, overwhelming Batman in such a way also teaches his foe to err on the side of caution. He has to know that even with his outstanding abilities, killing Batman wouldn't be easy -- but he is off to a good start.