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The really "cut proof" gloves are made from stainless steel links - like chain mail. The will protect against slicing cuts, I don't think they protect against piercing. I think protective gloves come in four basic components. There are standards for industry for specific types of activities. Fiber based gloves are low on the protection scale.
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I have been sharpening my chains by hand for 16 years now and have yet to cut myself, and I don't wear gloves. With the saw in a vise it's pretty safe, with a bit of care and attention.
Zach
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If you're right handed, sharpen the right side cutters first. Then, if your hand slips and a finger jambs into one of the left cutters, at least it's not sharp.
On cut resistant gloves: I wanted some to use with a roller/folder https://www.youtube.com/watch?v=5kfqmn8hd40 for sheetmetal work, but had to try at least a half dozen types before I found some that fit my hands well enough to be able to work in. They don't have as much stretch, or give as other types of work gloves. I can't imagine I could wear any of them for carving wood.