Because, he was married to Jaya and was the father of her kids - Shweta and Abhishek.
Rekha, Amitabh and Jaya in “Silsila”
Amitabh and Jaya’s marriage was not an arranged marriage. Amitabh and Jaya were in love since the time Amitabh saw Jaya on the set of film “Guddi”.
Amitabh at that time was a struggling actor trying to make his mark in the film industry while Jaya was an established star.
No one including Amitabh knew about the future of his movie carrier. Most of the people had written him off as his films flopped one after the other - almost a dozen films performed poorly at the box office before he could find success with iconic “Zanjeer”.
During his struggle phase, Jaya was a huge support for Amitabh. She adored him and loved him. During shooting of the film “Bawarchi”, Rajesh Khanna, who was reining superstar at that time asked his co-star, Jaya Bhaduri - why is she wasting time on a person like Amitabh who seems to have no future in the film industry?
To which Jaya replied angrily - One day, Amitabh will be much more successful and bigger star than you.
Jaya’s words were so prophetic. Amitabh rose in stardom while Rajesh Khanna became a flop star in late 70s.
In Zanjeer (1973), when no established actress was willing to work with Amitabh considering that he was a newcomer, Jaya agreed to work as heroine of Amitabh in the movie. The point is Jaya has done a lot for Amitabh. She is not just a wife but a friend and a support system as well.
Year 1975 brought enormous success to Amitabh as his two movies Sholay and Deewar became box office blockbusters and went on to achieve legendary status in future.
Amitabh had arrived; there was no one who could challenge Amitabh in second half of the seventies.
This was the time when Amitabh met Rekha on the set of movie “Do Anjaane” (1976).
It was mutual love and they started meeting each other in private. This has been confirmed by many of Rekha’s co-stars and directors.
Actor Ranjeet said that Rekha wanted her evenings free while shooting a movie with him as she wanted to spend evening time with Amitabh.
Director Yash Chopra also confirmed in an interview that Amitabh and Rekha were in a relationship before “Silsila”
Rekha herself admitted her love for Amitabh in numerous interviews.
Though Amitabh never accepted the relationship publicly as he was married to Jaya all this while.
Rekha said that he did what he had to do to protect his image and his family.
Also, Amitabh owes a lot to Jaya as she was the one who believed in him in his early years when everyone else was sceptical of Amitabh’s acting prowess.
If we closely observe Amitabh, he has been a very cautious and risk averse person in his entire life. He doesn't go to the extremes. He has this inclination for stability, status quo and settlement.
When Amitabh was threatened by Shiv Sena chief Bal Thackeray for his alleged involvement in Bofors scam, he went to Matoshree (Thakeray’s abode) for Thackeray’s blessings.
Bal Thackeray and Amitabh Bachchan
When Jaya Bachchan said - Gandhi family betrayed us, Amitabh immediately issued a statement that Gandhis are kings and Bachchans are subjects, how can they be friends.
Amitabh doesn't like confrontation; he always goes for the compromise and tries to resolve the matter then and there itself.
With Rekha, he again chose the same path - path of stability, status quo and continuity of his marriage with Jaya.
He is not a person who will go to extreme length for his political ideology or for his love for that matter.
He will always take a U-turn if going becomes tough.
Same thing he did in politics. The moment his name cropped up in Bofors scandal and he was subjected to media scrutiny, he decided to withdraw from politics for ever. He didn't fight it out while being there in the political system. He chose to exit while his best friend Rajiv Gandhi was the prime minister at that time.
Rajiv Gandhi and Amitabh
With Rekha, he went ahead as he loved her but he didn't want to divorce Jaya and make their children’s life difficult. He wanted to come across as a family man who respected his parents, loved his kids and got along with his wife.
Given the situation and his mental makeup, eventually he didn't marry Rekha.