Whilst you can use inconsistency as grounds to appeal you cannot legally challenge this any further. This is due to your length of service - if you have been continuously employed at your place of work for less than 2 years then your employment rights will unfortunately be somewhat limited. Most importantly, you will not be protected against unfair dismissal. This means that your employer can dismiss you for more or less any reason, and without following a fair procedure, as long as their decision is not based on a reason which makes a dismissal automatically unfair, such as discrimination due to a protected characteristic (i.e. because of gender, race, religion, age, disability, sexual orientation, etc.).
The argument of inconsistency is something which can only be challenged under the unfair dismissal argument so as you do not have the legal protection to challenge that. Therefore, you are entirely free to raise it in the appeal but the employer is not obliged to consider it so from now it is very much down to them,
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