A purpose of a Notice of Admit is to attempt to narrow down the contentious circumstances in a matter, in an effort to save the parties and the court time in leading evidence to support certain facts. For simple example: One party serves a Notice to Admit to the other party claiming that the events occurred during the day on the 30th of December 2020 (two separate facts which may have been contentious). The other party admits the events occurred on 30 December, but not that they occurred during the day. When the matter comes to trial, the parties hand up a statement of agreed facts that the events occurred on that date. Assuming acceptance by the Court then there is no need for either party to prove the date the events occurred - but it would still be contentious as to what time of day they occurred.
It would appear in your circumstances that the other side wants you to prove your contentions. This could be for a number of reasons. Perhaps the evidence doesn't prove what you think it does, or it could be inadmissible. Ultimately, if you bear the burden of proof then it is your obligation to lead evidence to substantiate the necessary facts/elements. If they don't admit a fact that is clearly relevant and demonstrably true then there are potential costs consequences that flow from it.