You will forget to wrap the object with {}.
$scope.product.assets.key.push(
name : asset[0],
additionalPrice : asset[1],
file : asset[2],
attribute : asset[3]
);
try it
$scope.product.assets.key.push({
name : asset[0],
additionalPrice : asset[1],
file : asset[2],
attribute : asset[3]
});
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