Abuela and Mirabel didn't see eye to eye at the beginning of Encanto, and here's why. The distanced gap between the matriarchal grandmother and her granddaughter is shown when Mirabel seemingly doesn't receive a magical gift. Abuela treasures the ceremony in which the future generations get their gift, and when Mirabel doesn't receive one, she becomes cold towards her, despite not overtly having a gift herself. She is also harsh on other members of the Madrigal family, but Mirabel becomes distinctively left out. There may be a deeper reason as to this dislike.
Abuela is the matriarch of the Madrigals, and in many ways, of the townspeople too. She appears to be strong, put-together, and a natural leader who takes things in her stride, constantly trying to make the town a happy and easy place to live. In the beginning, it is clear that Pedro, Abuela Alma's husband, has passed away, but it isn't clear how until later. This trauma may play a part in why she doesn't warm to Mirabel.
If the theories that Mirabel and Abuela have the same hidden gift are to be believed, this may be why Abuela doesn't really like Mirabel at the beginning of Encanto. As stated, neither character has an overt gift in the film (with Mirabel possibly sabotaging her gift) and serve as the only two members of the Madrigal family who are power-less. It is speculated that Abuela and Mirabel's hidden gift is that they have the ability to keep the family's magic going, mirroring each other in this way.
By sharing the same concealed magical gift, Mirabel possibly reminds Abuela too much of herself. Looking at Mirabel, she perhaps sees and relives the trauma that happened years ago when the magic began. Abuela witnessing the violent death of her husband and then being forced to raise triplets without him was the event that brought about the Madrigal magic, and while it was a wonderful offering, it wasn't without its sadness, especially as the events actually mirror real Colombian history. By possibly sharing the same gift, the reflection of herself in her granddaughter brings about the residue of this unresolved trauma. Thus, Abuela treats Mirabel harshly because she treats herself harshly. She puts an undue amount of pressure on herself to keep the family going in times of crisis by performing the role of a strong figurehead, trying to overcompensate with a sense of power and control because she had none over her husband's death. At the end of the Encanto, Mirabel and Abuela reconcile, which is only possible once Abuela has shared her trauma and begins working on herself. As Abuela addresses her past, she finally softens towards Mirabel.
By symbolically passing the candle down to Mirabel as Abuela's replacement, it signals Abuela being ready to accept her past and her future, which benefits all members of the Madrigals in Encanto. If Mirabel had gotten a gift, it could have only served as a distraction for Abuela, and she might not have processed her past. But, by having Mirabel in the exact same position as Abuela, both power-less, Abuela is forced into introspection and really had to see herself. It is because the pair heal the cracks in their own relationship that Casita can be rebuilt, and the family can continue to grow.