Your problem has more than one aspect, which is also why you basically have two questions in your post:
Where do requirements end and design begin?
and
When are these discussions appropriate?
I'll address these questions separately:
Where do requirements end and design begin?
Taken literally, the answer to this question is question is: Requirements don't end when design begins. Once you have completed your initial requirements, it is highly likely that they will change, so you need to implement a change process (e.g. a change review board in classical project managment or maintenance of the product backlog in SCRUM). Also, when your product design is completed, you need to verify it against the requirements.
I understand your question though in the sense of "When do inital requirements end?". The answer is: It depends on your project approach. If you are using a classical approach like waterfall or the V-model, the answer is: once the requirements specification is completed. If you are using an agile approach (such as XP or SCRUM), requirements and design run in parallel. You are preparing the requirements for the next iteration while the developers implement the current requirements.
When are these discussions appropriate?
I admit that the first part of the answer is a bit technical, and I can see that youir real problem lies in the way requirements are drafted. To answer the question, it depends on which requirements you are working on:
- The high-level business requirements.
- The lower level application requirements.
If you are working on the business requirements, you want less technical aspects than when working on the application requirements. The reason is quite simple: the higher your requirements level is, the further you are away from the implementation and the less these things matter.
In practice I have rarely seen this kind of distinction; you usually talk about "the requirements". And how much design details you want in your requirements depends on a number of factors, for example:
- What kind of system are your building? When you build an operating system, you can not craft the requiremenst without a lot of technical details.
- Company culture. A tech company will see the definition of what is a requirement differently than a retail company.
- The project team. Developers see requiremens differently than business analysts and depending on your team composition there will be different outputs.
Especially in lower-level requirements, technical details are not always a bad thing. For example:
- If a requirement says that the designed webpage should use responsive webdesign, it is probably OK. Although this is a technical term, it describes very well what is desired as an output.
- On the other hand, purely technical details like choice of programming language don't belong into requirements.
To disagree on what is requirement and what is implementation detail is quite common. I though have made the opposite experience: product managers often try to limit the definitin on "what is a requirement" to offload the detail work to the development team (let's face it: requirements are hard).
The best answer I can give you is: Address your issue openly with the team. Whether you are the only one seeing matters like this or others agree with you, you have a valid point. You should figure out some guidelines on what is a requirement (you can also write them down for reference), so that everyone is on the same page. If your team works well, you won't need any moderation, since you will be able to work it out together. Since there is a grey area, you will find a solution that probably everyone will be able to live with. If you have some friction in your team, you should nominate a moderator that everyone accepts as neutral. Or even better: try to work out your friction, since that will benefit the project in other aspects, too.
You should also make sure to include the members of your team who will use the requirements specification (developers, testers etc.) in your discussion. They will have to work with the specification, so their point of view matters. What would also be benefitial is to review the requirements document including (but not only) these stakeholders. The review serves as a corrective in case the requirements err too much into the technical implementation.
Once you have clearly defined what is a requirement, you should be able to draft a requirements document everyone is happy with. A review will correct any issues that remain.