Want rule three in full detail?
The single change that made the biggest difference to how quickly a miss stops mattering.
Read the instant restart method1v1 against your own kid is oddly the highest-pressure version of football in the garden, and it doesn't need to be.
There's something about it being just the two of you that ramps things up. In a bigger group game there's always somewhere to hide for a minute. In 1v1, every touch is watched by exactly one person, and that person is you. If your child seems more tense in 1v1 than in anything else you play, that's not unusual, and it's fixable with a few ground rules on your side rather than theirs.

Four ground rules for you
Play at about 70%. Not letting them win outright, children can usually tell, but genuinely not trying your hardest either. Let a few things go past you that you could have stopped. The goal isn't for them to win every time, it's for the gap between "trying" and "actually beating me" to feel closeable.
Narrate it like commentary, not coaching. "Ooh, nearly had that one" keeps the mood playful. "You need to shield the ball better" turns a game into a lesson, which is exactly what 1v1 doesn't need more of.
Keep rounds short and reset often. Play to one goal, then start again, rather than one long grinding contest. Frequent fresh starts mean any one mistake matters less, because the next round is only seconds away.
Skip the running score unless they ask for it. If your child brings up the score themselves, go with it. If they don't, don't introduce it. Plenty of the value in 1v1 is just the shared attention, not the result.

If it still doesn't land
If you try all of this and your child still seems to deflate during 1v1 specifically, that's worth noticing rather than pushing through. Some children do better with a game that has a bit more going on, a target, a gate, a partner rather than an opponent, and there's no reason 1v1 has to be the format you reach for every time.

Pairs well with
Frequent fresh starts, rule three above, is really the instant restart method applied to 1v1 specifically. It does a lot of the pressure-lowering work inside any game, 1v1 included, because the shorter the gap between a miss and the next go, the less time there is for tension to build. See how Our Kickabout researches its pages.
Keep going
The single change that made the biggest difference to how quickly a miss stops mattering.
Read the instant restart methodThree mistake-proof scoring systems if your child does want a number to chase.
Read mistake-proof scoring systemsStart with the wider confidence ladder and a five-minute first game.
Return to Confident BeginnersTonight's five minutes
Short rounds, playful commentary, no running score unless they ask.