You’ve gone through the interview process and have ultimately ‘landed’ the job. You were looking to leave your current employer for some reason or else you would have never wasted your time to interview elsewhere.
Upon giving notice to your current employer, they try to entice you to stay- money, benefits- etc. While that may be great for the short term- you have already put in question your loyalty to the organization for the long-term.
Great article by Robin Judson of Robin Judson Partners on why it is important to NEVER accept a counter offer-