Why does Cersei say that she killed her husband?

Question

In Game of Thrones Season 6 Episode 10, while torturing Septa Unella, Cersei says these words:

Beating me, starving me, frightening me, humiliating me. You didn't do it because you cared about my atonement. You did it because it felt good.
I understand.
I do things because they feel good.
I drink because it feels good.
I killed my husband because it felt good to be rid of him.
I fuck my brother because it feels good to feel him inside me.
I lie about fucking my brother because it feels good to keep our son safe from hateful hypocrites.
I killed your High Sparrow and all his little sparrows all his septons, all his septas, all his filthy soldiers, because it felt good to watch them burn.

I understands that Cersei is confessing these things as no one can do anything now to her. She says these to Septa to show how powerful she is now.

Most of the things she said are true but why is she saying she killed her husband, While we know that Robert died during the hunt fighting with a boar? How come Cersei is responsible for that? Indeed she had the most benefit from the death of Robert, but how is she responsible for that?

Answer 1

It was more of a brilliant plan orchestrated by Cersei. She just created the most convenient environment to ensure Robert Baratheon is killed / gets himself killed without directly implicating herself in a murder.

If he didn't die, it would just be an injury and she could try another time. If he died, he would be out of her way with nothing pointing to her.

Hunting and drinking are both things that Robert likes, but to do both of them at once may easily result in an accident. She just created the situation where she got Lancel Lannister to get Robert highly drunk before the hunt. Robert, being more drunk than usual, couldn't handle the boar all by himself and got himself fatally injured.

Now the reasons she would do this is:

1. She had a secret over her head (her kids actually being fathered by Jaime Lannister) that would topple her position as a queen.
2. She is a power-hungry person who would do anything to get to the top.
3. She wanted to instate her son as the king and do her bidding through her son.

So yeah if her plan was to get Robert highly intoxicated hoping he would get himself killed or fatally injured, she basically attempted to murder him (and succeeded) which makes her claim "I killed my husband" true.

Answer 2

As the plan is already is explained in other answer. I am just adding some things I found during my research to confirm same.

Lord Varys 'Spider' also implies same that King Robert's squire Lancel Lannister has given more wine to the king than usual. Master of Whispers Varys is notorious for knowing such information.

Barristan Selmy: He was reeling from the wine. He commanded us to step aside, but I failed him.

Ned Stark: No man could have protected him from himself.

Lord Varys: I wonder, Ser Barristan, who gave the king this wine?

Barristan Selmy: His squire, from the king's own skin.

Ned Stark: His squire? The Lannister boy?

Lord Varys: Such a dutiful boy to make sure his Grace did not lack refreshment. I do hope the poor lad does not blame himself.

Ned Stark: His Grace has had a change of heart concerning Daenerys Targaryen.

Source for script

Also, Lancel is shown to be sleeping with queen Cersei a few days later, so it can be deduced that she has asked him to make sure the king's senses are dulled during the hunt.

This confession basically confirms the murder plot directed at the king as implied in Season 1.