They say “he is too old” because he’s already spent too much time in the dangerous outside world that he instinctually suppresses his emotions. Because what many people misunderstand about the scene is that they didn’t say no to Anakin joining the order because he was afraid (even Jedi Masters can be afraid; Yoda even says later in the movie that he’s afraid for Anakin’s training), they said no because he refused to admit that he’s afraid. When the Jedi were basically telling him, “Dude, we can read you’re mind, we know you’re afraid”, he continues to say he’s not. Part of the Jedi way is confronting fear and overcoming it (this is stated by Lucas), but you can’t overcome something you refuse to acknowledge exists. And it’s because of this that his fear continued to eat him up.
George Lucas has explicitly said the reason Jedi are trained from birth is so they never gain a habit in holding onto emotions or suppressing them. They’re trained from birth to let go. That’s why they say he’s too old.
Anakin wasn’t stretching the truth or lying when he said they’re encouraged to love. George Lucas has not only said that Jedi are allowed to love and should love everybody but he’s also said Jedi Knights aren’t celibate. What is forbidden for a Jedi is attachment, AKA possessive relationships. Lucas basically uses the Buddhist definition of attachment. What is forbidden is what Anakin did: putting your relationship over the greater good. Being so attached that you let it get in the way of the mission (when he almost ditches the mission to save Padme at the end of AOTC) and being willing to basically sell your soul to the devil and slaughter all the Jedi including the children because you refuse to let go of your wife. Anakin either knows but refuses to admit that he’s gotten too attached to Padme beyond a healthy degree or his emotions are so clouded he just doesn’t know the difference between love and attachment (as defined by Lucas).
This is explored in the Clone Wars: Obi-Wan loved Satine, and he wasn’t forced to suppress those feelings. But he never let it cloud his judgement or get in the way of the greater mission, and when it did (when he rushed to Mandalore to rescue her), it had dire consequences, and she died. “It’s not that we’re not allowed to have these feelings, it’s natural.” And if he wanted to pursue that relationship, he would’ve needed to leave the Jedi Order (because again, when you’re in a position in which trillions of lives depend on you, you can’t be imbalanced).
Now I will admit this stuff is muddled in the films due to Lucas’ flat style of writing dialogue (he doesn’t really take the time to properly explain these intricate details), but those are the intentions of the author, as shown by the many times he’s been quoted to say this kind of stuff.