А так удаляется только тот, что нужен
<body>
<div data-day="16" data-month="9">16</div>
<script>
const fromStorage =[{
"day": "2",
"month": "9"
}, {
"day": "9",
"month": "9"
}, {
"day": "16",
"month": "9"
}, {
"day": "5",
"month": "10"
}, {
"day": "12",
"month": "10"
}, {
"day": "16",
"month": "10"
}, {
"day": "19",
"month": "10"
}];
const e = document.querySelector('div');
e.addEventListener('click', () => {
console.log(fromStorage.length);
let filtered = fromStorage.filter(o => {
return !(o.day === e.dataset.day && o.month === e.dataset.month)
});
console.log(filtered)
})
</script>
</body>