Accumulated depreciation is the grand total of all depreciation expense that has been recognized to date on a fixed asset. As such, it is considered a contra asset account, which means that it contains a negative balance that is intended to offset the asset account with which it is paired, resulting in a net book value. Accumulated depreciation is classified separately from normal asset and liability accounts, for the following reasons:
It is not an asset, since the balances stored in the account do not represent something that will produce economic value to the entity over multiple reporting periods. If anything, accumulated depreciation represents the amount of economic value that has been consumed in the past.
It is not a liability, since the balances stored in the account do not represent an obligation to pay a third party. Instead, accumulated depreciation is used entirely for internal record keeping purposes, and does not represent a payment obligation in any way.
If you must make a choice between classifying accumulated depreciation as an asset or liability, it should be considered an asset, simply because that is where the account is reported in the balance sheet. If it were to be categorized as a liability, this would create the incorrect impression that the business has a liability to a third party.