if I was an anti-gun person and saw this I wouldn’t be swayed to the pro-gun side

It's a dumb premise to begin with. Whoever made that pic is either really dumb or is just trolling. The majority of firearm related deaths in the US are suicides, to start. Secondly, the murders committed by firearms are mostly gang related shootings. Dozens of people in the US are gunned down every week due to gang activity.

Mass shootings like the huge ones like the Orlando night club or Las Vegas, as unprecedented as they may be in context of single events, still make up a tiny minority of firearm homicides. They happen once every couple of years, whereas dozens of people are shot dead every week from the drug trade/etc.

So it's not even an argument of "freedom vs children's lives" to begin with.