Thank you for your question today, I look forward to assisting you. I bring nearly 20 years of legal experience in various disciplines.
Unless you have some sort of contract which requires first that you can only be terminated for cause and second that you actually receive some sort of severance, you're really not in any sort of legal position to negotiate severance at all.
Severance is not required in any state or federal law, so it is only paid in one of three instances.
1. The company is breaching a contract of employment that requires that you can only be terminated for cause or they are contractually obligated to pay it. Then, the threat is suit for breach of the contract and then you'd be able to negotiate.
2. You have some sort of discrimination claim against them that they would take seriously, such that they want to buy a "waiver of suit" from you. So, if you have any evidence that the basis for your separation would your race, religion, gender, age, disability or FMLA use, then you can use the legitimate threat of a suit in order to negotiate.
3. The company simply wants to be fair with you and pay something. Here, there is no room for negotiation because the entire basis for the severance is the employer's goodwill...which may be reduced by a demand for more than is originally offered.
While I certainly understand your concern about lack of training and moving forward in the industry while working with them, that doesn't create any legal leverage at all to negotiate severance.