"but he's kind of highlighting the issue when he could just sit and not look"
This thread speaks absolute volumes about how breastfeeding is perceived in the UK, and probably why breastfeeding continuation rates are so low.
The bottom line on this thread seems to be this:
- it's absolutely reasonable to find breastfeeding embarrassing. And it's reasonable to find breastfeeding embarrassing because you know, it involves BREASTS, which are sexual, and nudity, which is, um, a bit disgusting or risque.
- it's absolutely reasonable to make your discomfiture with breastfeeding apparent to a vulnerable woman who is learning to breastfeed.
Every time the OP's dad gets up and leaves the room when she breastfeeds, he's drawing attention to the fact that he sees breastfeeding as an indecent/sexual/embarrassing act.
Thanks dad! 
"Well no, because it's a stupid bloody comparison to make minifingerz. It's not comparable."
Sorry - it's a very good comparison.
Many older people are unfamiliar around open displays of affection between homosexual couples because they grew up in a culture where homosexuality was unacceptable and hidden. Hence many may feel unsettled by the sight of gay couples showing affection to each other.
Many people in the UK have also grown up in a society where normal, unselfconscious breastfeeding - as practiced by 90% of the rest of the world - is a culturally uncommon sight, and where there is a sexual fixation on breasts. Hence many may feel uncomfortable around a mother who is breastfeeding.
In both cases the reaction of discomfiture is triggered by unfamiliarity and cultural ignorance, rather than a rational response to indecency (neither breastfeeding nor normal displays of affection like hand-holding or kissing are intrinsically indecent).
In both cases it's understandible that someone may find the sight of a breastfeeding mother/gay couple holding hands emotionally challenging, however, it's only in the case of breastfeeding that making your discomfiture obvious by constantly leaving the room every time it happens, morally acceptable.